The circumference of a sphere was measured to be 80 cm with a possible error of 0.5 cm.

1) Use differentials to estimate the maximum error in the calculated volume. (Round your answer to the nearest integer.)

2) What is the relative error? (Round your answer to three decimal places.)

1. 👍 0
2. 👎 0
3. 👁 420
1. v = 4/3 pi r^3
dv = 4 pi r^2 dr

c = 2pi r
dc = 2pi dr
so, dr = dc/(2pi)
meaning that

dv = 4 pi r^2 dc/(2pi)
= 2 r^2 dr

so, using the given numbers,

dv = 2*(80/2pi)^2 * 0.5 = 1600/pi^2

1. 👍 0
2. 👎 0
posted by Steve

## Similar Questions

1. ### Calculus

The circumference of a sphere was measured to be 74 cm with a possible error of 0.5 cm. Use linear approximation to estimate the maximum error in the calculated surface area.

asked by Salman on November 6, 2009
2. ### Calculus

The circumference of a sphere was measured to be cm with a possible error of cm. Use linear approximation to estimate the maximum error in the calculated surface area.

asked by Salman on November 6, 2009
3. ### Calculus

The circumference of a sphere was measured to be 81 cm with a possible error of 0.5 cm. Use linear approximation to estimate the maximum error in the calculated surface area

asked by Emely on November 8, 2011
4. ### math

The circumference of a sphere was measured to be 82 cm with a possible error of 0.5 cm. Use linear approximation to estimate the maximum and relative error in the calculated surface area.

asked by bobby on April 6, 2012
5. ### math

he circumference of a sphere was measured to be 78000 cm with a possible error of 050000 cm. Use linear approximation to estimate the maximum error in the calculated surface area.

asked by jin on August 27, 2010
6. ### Calculus

The circumference of a sphere was measured to be 74.000 cm with a possible error of 0.50000 cm. Use linear approximation to estimate the maximum error in the calculated surface area

asked by Julie on July 20, 2011
7. ### Calculus

The circumference of a sphere was measured to be 81000 cm with a possible error of 050000 cm. Use linear approximation to estimate the maximum error in the calculated surface area.

asked by Emely on November 8, 2011
8. ### calculus

The radius of circular disk is 18cm with a maximum error of 0.2cm. Estimate the maximum error in calculated area of the disk. b) The circumference of a sphere was measured to be 64cm with a maximum error of 0.5. Estimate the

asked by funmi on January 22, 2015
9. ### Math

The circumference of a sphere was measured to be 74.000 cm with a possible error of 0.50000 cm. Use linear approximation to estimate the maximum error in the calculated surface area. Estimate the relative error in the calculated

asked by Victoria on October 5, 2014
10. ### CALCULUS

The circumference of a sphere was measured to be 83000 cm with a possible error of 050000 cm. Use linear approximation to estimate the maximum error in the calculated surface area. ________________ Estimate the relative error in

asked by Sarah on May 19, 2012

More Similar Questions