Solucionario del Iibro Fisica universitaria dé sears-zemansky 12va edicion. 1. 1-1 Systems, PHYSICAL Amounts AND VECTORS 1.1. IDENTIFY: Convert devices from mi tó km and fróm km to ft. Place UP: 1 in. 2.54 cm=, 1 km = 1000 michael, 12 in. 1 ft=, 1 mi = 5280 ft.

• Algebra Lineal Stanley Grossman 7 Edicion Solucionario 1
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EXECUTE: (a) 2 3 5280 ft 12 in. 2.54 cm 1 michael 1 kilometres 1.00 mi (1.00 mi) 1.61 km 1 mi 1 ft 1 in. 10 cm 10 michael ⎛ ⎞⎛ ⎞⎛ ⎞⎛ ⎞⎛ ⎞ = =⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠⎝ ⎠⎝ ⎠⎝ ⎠ (b) 3 2 310 meters 10 cm 1 in. 1 ft 1.00 kilometres (1.00 km) 3.28 10 ft 1 kilometres 1 michael 2.54 cm 12 in. ⎛ ⎞⎛ ⎞⎛ ⎞⎛ ⎞ = = ×⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠⎝ ⎠⎝ ⎠ EVALUATE: A mile will be a higher distance than a distance. There are usually 5280 ft in a mile but only 3280 ft in a kilometres.

IDENTIFY: Convert volume products from T to 3 in. Place UP: 3 1 T 1000 cm=. 2.54 cm= EXECUTE: 33 31000 cm 1 in. 0.473 T 28.9 in. 1 M 2.54 cm ⎛ ⎞ ⎛ ⎞ × × =⎜ ⎟ ⎜ ⎟ ⎝ ⎠⎝ ⎠ EVALUATE: 3 1 in.

Is certainly better than 3 1 cm, so the volume in 3 in. Is definitely a smaller amount than the quantity in 3 cm, which is certainly 3 473 cm. IDENTIFY: We know the rate of light in michael/s. Switch 1.00 ft to m and t from t to ns. SET UP: The quickness of light is definitely 8 3.00 10 meters/sv = ×. 1 ft 0.3048 michael=. 9 1 s 10 ns=.

Perform: 9 8 0.3048 m 1.02 10 t 1.02 ns 3.00 10 michael/s t − = = × = × EVALUATE: In 1.00 s i9000 light travels 8 5 5 3.00 10 m 3.00 10 kilometres 1.86 10 mi× = × = ×. IDENTIFY: Convert the units from g tó kg and fróm 3 cm to 3 meters. SET UP: 1 kg 1000 g=. 1 m 1000 cm=. Perform: 3 4 3 3 gary the gadget guy 1 kg 100 cm kg 11.3 1.13 10 cm 1000 h 1 m meters ⎛ ⎞ ⎛ ⎞ × × = ×⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ EVALUATE: The percentage that changes cm to m is certainly cubed, because we require to transform 3 cm to 3 meters.

IDENTIFY: Convert quantity units from 3 in. Place UP: 3 1 D 1000 cm=. EXECUTE: ( ) ( ) ( )33 3 327 in. 1 L 1000 cm 5.36 T× × = EVALUATE: The volume can be 3 5360 cm.

3 1 cm can be much less than 3 1 in., so the volume in 3 cm is a bigger quantity than the volume in 3 in. IDENTIFY: Convert 2 ft to 2 m and then to hectares.

Place UP: 4 2 1.00 hectare 1.00 10 m= ×. 1 ft 0.3048 michael=. Implement: The region can be 22 4 2 43,600 ft 0.3048 michael 1.00 hectare (12.0 acres) 4.86 hectares 1 acre 1.00 ft 1.00 10 m ⎛ ⎞⎛ ⎞ ⎛ ⎞ =⎜ ⎟⎜ ⎟ ⎜ ⎟ ×⎝ ⎠ ⎝ ⎠⎝ ⎠. EVALUATE: Since 1 ft 0.3048 m=, 2 2 2 1 ft (0.3048) m=. IDENTIFY: Convert seconds to decades. SET UP: 9 1 billion secs 1 10 s i9000= ×.

EXECUTE: ( )9 1 h 1 time 1 con 1.00 billion seconds 1.00 10 beds 31.7 y 3600 s 24 l 365 days ⎛ ⎞⎛ ⎞⎛ ⎞ = × =⎜ ⎟⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠⎝ ⎠. 1. 1-2 Part 1 EVALUATE: The transformation 7 1 y 3.156 10 t= × takes on 1 y 365.24 deb=, which will be the average for one extra time every four yrs, in leap yrs. The issue says instead to presume a 365-time 12 months.

IDENTIFY: Apply the provided conversion elements. Collection UP: 1 furlong 0.1250 mi and 1 fortnight 14 days.= = 1 time 24 h.= Perform: ( ) 0.125 mi 1 fortnight 1 time 180,000 furlongs fortnight 67 mi/h 1 furlong 14 times 24 h ⎛ ⎞⎛ ⎞⎛ ⎞ =⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠⎝ ⎠ EVALUATE: A furlong will be much less than a miIe and a fórtnight is definitely many hours, so the speed limit in mph will be a significantly smaller number. IDENTIFY: Transfer miles/gallon to km/T. SET UP: 1 mi 1.609 km=. 1 gallon 3.788 D.= EXECUTE: (a) 1.609 kilometres 1 gallon 55.0 kilometers/gallon (55.0 miles/gallon) 23.4 kilometres/L 1 mi 3.788 T ⎛ ⎞⎛ ⎞ = =⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠. (c) The volume of gas required will be 1500 kilometres 64.1 L 23.4 kilometres/L =.

64.1 T 1.4 tanks 45 L/tank =. EVALUATE: 1 mi/gal 0.425 kilometres/L=. A km is extremely roughly fifty percent a mile and there are usually roughly 4 liters in a gallon, so 2 4 1 mi/gal km/L∼, which is definitely roughly our result. IDENTIFY: Change units. Collection UP: Make use of the unit conversions provided in the issue.

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Also, 100 cm 1 meters= and 1000 h 1 kg=. Perform: (a) mi 1h 5280 ft ft 60 88 l 3600s 1mi s ⎛ ⎞ ⎛ ⎞⎛ ⎞ =⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ (n) 2 2 ft 30.48cm 1 m michael 32 9.8 s 1ft 100 cm h ⎛ ⎞⎛ ⎞ ⎛ ⎞ =⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠⎝ ⎠ (chemical) 3 3 3 3 g 100 cm 1 kg kg 1.0 10 cm 1 m 1000 gary the gadget guy m ⎛ ⎞⎛ ⎞ ⎛ ⎞ =⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ EVALUATE: The relations 60 mi/l 88 ft/h= and 3 3 3 1 gary the gadget guy/cm 10 kg/michael= are exact.

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The relationship 2 2 32 ft/s 9.8 meters/s= is certainly accurate to only two significant statistics. IDENTIFY: We know the density and bulk; hence we can find the volume making use of the connection density bulk/volume /meters Sixth is v= =. The radius is then discovered from the quantity formula for a sphere and the result for the volume. SET UP: 3 Density 19.5 g/cm= and essential 60.0 kg.meters = For a world 34 3 Sixth is v urπ=. Carry out: 3 critical 3 60.0 kg 1000 g /density 3080 cm 19.5 h/cm 1.0 kg V meters ⎛ ⎞⎛ ⎞ = = =⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠. ( )33 3 3 3 3080 cm 9.0 cm 4 4 V r π π = = =. EVALUATE: The density will be really large, so the 130 pound sphere is small in size.

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IDENTIFY: Use your calculator to display 7 10π ×. Compare that amount to the amount of mere seconds in a calendar year. SET UP: 1 month 365.24 times,= 1 time 24 l,= and 1 l 3600 beds.= EXECUTE: 724 l 3600 s (365.24 days/1 year) 3.15567. 10 beds 1 time 1 l ⎛ ⎞⎛ ⎞ = ×⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠; 7 7 10 s i9000 3.14159.

10 s i9000π × = × The approximate expression is definitely accurate to two substantial figures. EVALUATE: The close agreement can be a numerical accident.

IDENTIFY: The percent error is certainly the mistake separated by the quantity. Collection UP: The length from Berlin to Rome is given to the nearest 10 km. EXECUTE: (a) 3 3 10 m 1.1 10%. 890 10 meters − = × × (t) Since the range was provided as 890 km, the overall length should become 890,000 metres. We understand the overall range to just three substantial statistics. EVALUATE: In this situation a quite small percent error offers disastrous outcomes. IDENTIFY: When amounts are multiplied or divided, the amount of significant figures in the outcome can be no higher than in the factor with the fewest significant numbers.

When we add or subtract quantities it is certainly the location of the decimal that matters. Units, Physical Amounts and Vectors 1-3 Collection UP: 12 mm has two significant statistics and 5.98 mm provides three substantial figures. Implement: (a) ( ) ( ) 2 12 mm 5.98 mm 72 mm× = (two substantial numbers) (c) 5.98 mm 0.50 12 mm = (furthermore two significant statistics) (d) 36 mm (to the nearest millimeter) (n) 6 mm (e) 2.0 (two substantial numbers) EVALUATE: The length of the rectangle is known only to the néarest mm, so thé solutions in parts (c) and (deb) are known only to the néarest mm. IDENTIFY ánd SET UP: In each case, estimate the accuracy of the dimension. Perform: (a) If a meter stay can measure to the néarest millimeter, the mistake will be about 0.13%. (t) If the chemical stability can calculate to the néarest milligram, the mistake will become about 3 8.3 10%.− × (d) If a handheId stopwatch (as opposéd to electric timing products) can calculate to the néarest tenth of á second, the error will be about 2 2.8 10%.− × EVALUATE: The percent errors are those credited just to the limit of precision of the dimension. IDENTIFY: Use the severe values in the piece's length and width to find the doubt in the region.

Place UP: The length could end up being as large as 5.11 cm and the width could become mainly because large as 1.91 cm. Perform: The region can be 9.69 ± 0.07 cm2. The fractional doubt in the area is 2 2 0.07 cm 0.72%, 9.69 cm = and the fractional questions in the duration and size are 0.01 cm 0.20% 5.10 cm = and 0.01 cm 0.53%. 1.9 cm = The sum of these fractional questions is usually 0.20% 0.53% 0.73%+ =, in agreement with the fractional uncertainty in the region. EVALUATE: The fractional uncertainty in a product of amounts is higher than the fractional uncertainness in any of the individual numbers.

IDENTIFY: Determine the typical volume and size and the uncertainness in these amounts. SET UP: Using the intense ideals of the input data gives us the Iargest and smallest values of the target variables and from these we obtain the doubt. Carry out: (a) The quantity of a storage of size d and width t is certainly 2 ( /2).V d tπ= The average volume can be 2 3 (8.50 cm/2) (0.50 cm) 2.837 cm.V π= = But t is provided to only two substantial statistics so the solution should end up being portrayed to two significant statistics: 3 2.8 cm.Sixth is v = We can discover the doubt in the quantity as follows. The volume could end up being as large as 2 3 (8.52 cm/2) (0.055 cm) 3.1 cm,V π= = which is usually 3 0.3 cm larger than the typical worth. The volume could become as small as 2 3 (8.52 cm/2) (0.045 cm) 2.5 cm,V π= = which is usually 3 0.3 cm smaller than the typical value.

Solucionario del Iibro Fisica universitaria dé sears-zemansky 12va edicion. 1. 1-1 Systems, PHYSICAL Amounts AND VECTORS 1.1. IDENTIFY: Convert devices from mi tó km and fróm km to ft. Place UP: 1 in. 2.54 cm=, 1 km = 1000 michael, 12 in. 1 ft=, 1 mi = 5280 ft.

EXECUTE: (a) 2 3 5280 ft 12 in. 2.54 cm 1 michael 1 kilometres 1.00 mi (1.00 mi) 1.61 km 1 mi 1 ft 1 in. 10 cm 10 michael ⎛ ⎞⎛ ⎞⎛ ⎞⎛ ⎞⎛ ⎞ = =⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠⎝ ⎠⎝ ⎠⎝ ⎠ (b) 3 2 310 meters 10 cm 1 in. 1 ft 1.00 kilometres (1.00 km) 3.28 10 ft 1 kilometres 1 michael 2.54 cm 12 in. ⎛ ⎞⎛ ⎞⎛ ⎞⎛ ⎞ = = ×⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠⎝ ⎠⎝ ⎠ EVALUATE: A mile will be a higher distance than a distance. There are usually 5280 ft in a mile but only 3280 ft in a kilometres.

IDENTIFY: Convert volume products from T to 3 in. Place UP: 3 1 T 1000 cm=. 2.54 cm= EXECUTE: 33 31000 cm 1 in. 0.473 T 28.9 in. 1 M 2.54 cm ⎛ ⎞ ⎛ ⎞ × × =⎜ ⎟ ⎜ ⎟ ⎝ ⎠⎝ ⎠ EVALUATE: 3 1 in.

Is certainly better than 3 1 cm, so the volume in 3 in. Is definitely a smaller amount than the quantity in 3 cm, which is certainly 3 473 cm. IDENTIFY: We know the rate of light in michael/s. Switch 1.00 ft to m and t from t to ns. SET UP: The quickness of light is definitely 8 3.00 10 meters/sv = ×. 1 ft 0.3048 michael=. 9 1 s 10 ns=.

Perform: 9 8 0.3048 m 1.02 10 t 1.02 ns 3.00 10 michael/s t − = = × = × EVALUATE: In 1.00 s i9000 light travels 8 5 5 3.00 10 m 3.00 10 kilometres 1.86 10 mi× = × = ×. IDENTIFY: Convert the units from g tó kg and fróm 3 cm to 3 meters. SET UP: 1 kg 1000 g=. 1 m 1000 cm=. Perform: 3 4 3 3 gary the gadget guy 1 kg 100 cm kg 11.3 1.13 10 cm 1000 h 1 m meters ⎛ ⎞ ⎛ ⎞ × × = ×⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ EVALUATE: The percentage that changes cm to m is certainly cubed, because we require to transform 3 cm to 3 meters.

IDENTIFY: Convert quantity units from 3 in. Place UP: 3 1 D 1000 cm=. EXECUTE: ( ) ( ) ( )33 3 327 in. 1 L 1000 cm 5.36 T× × = EVALUATE: The volume can be 3 5360 cm.

3 1 cm can be much less than 3 1 in., so the volume in 3 cm is a bigger quantity than the volume in 3 in. IDENTIFY: Convert 2 ft to 2 m and then to hectares.

Place UP: 4 2 1.00 hectare 1.00 10 m= ×. 1 ft 0.3048 michael=. Implement: The region can be 22 4 2 43,600 ft 0.3048 michael 1.00 hectare (12.0 acres) 4.86 hectares 1 acre 1.00 ft 1.00 10 m ⎛ ⎞⎛ ⎞ ⎛ ⎞ =⎜ ⎟⎜ ⎟ ⎜ ⎟ ×⎝ ⎠ ⎝ ⎠⎝ ⎠. EVALUATE: Since 1 ft 0.3048 m=, 2 2 2 1 ft (0.3048) m=. IDENTIFY: Convert seconds to decades. SET UP: 9 1 billion secs 1 10 s i9000= ×.

EXECUTE: ( )9 1 h 1 time 1 con 1.00 billion seconds 1.00 10 beds 31.7 y 3600 s 24 l 365 days ⎛ ⎞⎛ ⎞⎛ ⎞ = × =⎜ ⎟⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠⎝ ⎠. 1. 1-2 Part 1 EVALUATE: The transformation 7 1 y 3.156 10 t= × takes on 1 y 365.24 deb=, which will be the average for one extra time every four yrs, in leap yrs. The issue says instead to presume a 365-time 12 months.

IDENTIFY: Apply the provided conversion elements. Collection UP: 1 furlong 0.1250 mi and 1 fortnight 14 days.= = 1 time 24 h.= Perform: ( ) 0.125 mi 1 fortnight 1 time 180,000 furlongs fortnight 67 mi/h 1 furlong 14 times 24 h ⎛ ⎞⎛ ⎞⎛ ⎞ =⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠⎝ ⎠ EVALUATE: A furlong will be much less than a miIe and a fórtnight is definitely many hours, so the speed limit in mph will be a significantly smaller number. IDENTIFY: Transfer miles/gallon to km/T. SET UP: 1 mi 1.609 km=. 1 gallon 3.788 D.= EXECUTE: (a) 1.609 kilometres 1 gallon 55.0 kilometers/gallon (55.0 miles/gallon) 23.4 kilometres/L 1 mi 3.788 T ⎛ ⎞⎛ ⎞ = =⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠. (c) The volume of gas required will be 1500 kilometres 64.1 L 23.4 kilometres/L =.

64.1 T 1.4 tanks 45 L/tank =. EVALUATE: 1 mi/gal 0.425 kilometres/L=. A km is extremely roughly fifty percent a mile and there are usually roughly 4 liters in a gallon, so 2 4 1 mi/gal km/L∼, which is definitely roughly our result. IDENTIFY: Change units. Collection UP: Make use of the unit conversions provided in the issue.

Algebra Lineal Stanley Grossman 7 Edicion Solucionario

Also, 100 cm 1 meters= and 1000 h 1 kg=. Perform: (a) mi 1h 5280 ft ft 60 88 l 3600s 1mi s ⎛ ⎞ ⎛ ⎞⎛ ⎞ =⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ (n) 2 2 ft 30.48cm 1 m michael 32 9.8 s 1ft 100 cm h ⎛ ⎞⎛ ⎞ ⎛ ⎞ =⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠⎝ ⎠ (chemical) 3 3 3 3 g 100 cm 1 kg kg 1.0 10 cm 1 m 1000 gary the gadget guy m ⎛ ⎞⎛ ⎞ ⎛ ⎞ =⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ EVALUATE: The relations 60 mi/l 88 ft/h= and 3 3 3 1 gary the gadget guy/cm 10 kg/michael= are exact.

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Algebra Lineal Stanley Grossman 7 Edicion Solucionario 1

The relationship 2 2 32 ft/s 9.8 meters/s= is certainly accurate to only two significant statistics. IDENTIFY: We know the density and bulk; hence we can find the volume making use of the connection density bulk/volume /meters Sixth is v= =. The radius is then discovered from the quantity formula for a sphere and the result for the volume. SET UP: 3 Density 19.5 g/cm= and essential 60.0 kg.meters = For a world 34 3 Sixth is v urπ=. Carry out: 3 critical 3 60.0 kg 1000 g /density 3080 cm 19.5 h/cm 1.0 kg V meters ⎛ ⎞⎛ ⎞ = = =⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠. ( )33 3 3 3 3080 cm 9.0 cm 4 4 V r π π = = =. EVALUATE: The density will be really large, so the 130 pound sphere is small in size.

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IDENTIFY: Use your calculator to display 7 10π ×. Compare that amount to the amount of mere seconds in a calendar year. SET UP: 1 month 365.24 times,= 1 time 24 l,= and 1 l 3600 beds.= EXECUTE: 724 l 3600 s (365.24 days/1 year) 3.15567. 10 beds 1 time 1 l ⎛ ⎞⎛ ⎞ = ×⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠; 7 7 10 s i9000 3.14159.

10 s i9000π × = × The approximate expression is definitely accurate to two substantial figures. EVALUATE: The close agreement can be a numerical accident.

IDENTIFY: The percent error is certainly the mistake separated by the quantity. Collection UP: The length from Berlin to Rome is given to the nearest 10 km. EXECUTE: (a) 3 3 10 m 1.1 10%. 890 10 meters − = × × (t) Since the range was provided as 890 km, the overall length should become 890,000 metres. We understand the overall range to just three substantial statistics. EVALUATE: In this situation a quite small percent error offers disastrous outcomes. IDENTIFY: When amounts are multiplied or divided, the amount of significant figures in the outcome can be no higher than in the factor with the fewest significant numbers.

When we add or subtract quantities it is certainly the location of the decimal that matters. Units, Physical Amounts and Vectors 1-3 Collection UP: 12 mm has two significant statistics and 5.98 mm provides three substantial figures. Implement: (a) ( ) ( ) 2 12 mm 5.98 mm 72 mm× = (two substantial numbers) (c) 5.98 mm 0.50 12 mm = (furthermore two significant statistics) (d) 36 mm (to the nearest millimeter) (n) 6 mm (e) 2.0 (two substantial numbers) EVALUATE: The length of the rectangle is known only to the néarest mm, so thé solutions in parts (c) and (deb) are known only to the néarest mm. IDENTIFY ánd SET UP: In each case, estimate the accuracy of the dimension. Perform: (a) If a meter stay can measure to the néarest millimeter, the mistake will be about 0.13%. (t) If the chemical stability can calculate to the néarest milligram, the mistake will become about 3 8.3 10%.− × (d) If a handheId stopwatch (as opposéd to electric timing products) can calculate to the néarest tenth of á second, the error will be about 2 2.8 10%.− × EVALUATE: The percent errors are those credited just to the limit of precision of the dimension. IDENTIFY: Use the severe values in the piece's length and width to find the doubt in the region.

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Place UP: The length could end up being as large as 5.11 cm and the width could become mainly because large as 1.91 cm. Perform: The region can be 9.69 ± 0.07 cm2. The fractional doubt in the area is 2 2 0.07 cm 0.72%, 9.69 cm = and the fractional questions in the duration and size are 0.01 cm 0.20% 5.10 cm = and 0.01 cm 0.53%. 1.9 cm = The sum of these fractional questions is usually 0.20% 0.53% 0.73%+ =, in agreement with the fractional uncertainty in the region. EVALUATE: The fractional uncertainty in a product of amounts is higher than the fractional uncertainness in any of the individual numbers.

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IDENTIFY: Determine the typical volume and size and the uncertainness in these amounts. SET UP: Using the intense ideals of the input data gives us the Iargest and smallest values of the target variables and from these we obtain the doubt. Carry out: (a) The quantity of a storage of size d and width t is certainly 2 ( /2).V d tπ= The average volume can be 2 3 (8.50 cm/2) (0.50 cm) 2.837 cm.V π= = But t is provided to only two substantial statistics so the solution should end up being portrayed to two significant statistics: 3 2.8 cm.Sixth is v = We can discover the doubt in the quantity as follows. The volume could end up being as large as 2 3 (8.52 cm/2) (0.055 cm) 3.1 cm,V π= = which is usually 3 0.3 cm larger than the typical worth. The volume could become as small as 2 3 (8.52 cm/2) (0.045 cm) 2.5 cm,V π= = which is usually 3 0.3 cm smaller than the typical value.