Math Calculus

A sphere is initially measured as having a radius of 4 inches. A subsequent measurement shows that the radius is really 3.99. Find (a) the actual difference in volume between the initial measurement and the correction, and (b) the difference as estimated through differentials. Note- the formula for the volume of a sphere is V=4/3(pi)r^3

I did question A, but I need help on question B...

thanks :)

  1. 👍 0
  2. 👎 0
  3. 👁 106
asked by Megan
  1. V = (4/3) pi r^3
    dV/dr = (4/3)3 pi r^2 = 4 pi r^2
    (which is the surface area of the sphere of course)
    so
    dV = 4 pi r^2 dr
    here dr = - .01
    so dV = -.01 * 4 * pi * 16
    dV = -2.01 in^3

    1. 👍 0
    2. 👎 0
    posted by Damon
  2. Thank you soo muccchh

    1. 👍 0
    2. 👎 0
    posted by Megan
  3. sorry actually i got that part which is part a. What I need is part (b). Find the delta(v)

    1. 👍 0
    2. 👎 0
    posted by Megan

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    If the radius and diameter of a sphere were measured in inches, then the surface area would be measured in

    asked by troy on November 21, 2010
  2. math

    A right circular cone is inscribed inside a sphere. The right circular cone has the radius of the base of 4 inches and the height is greater than 2 inches. The sphere has a radius of 5 inches. What is the ratio of the volume of

    asked by Jessica on March 6, 2011
  3. chemistry 1045L

    The volume of a sphere is given by V=(4)(3.14)(r^3)/3 where r is the radius of the sphere. what is the density in g/mL of a sphere which weighs 2.00lb and has a radius of 3.50 inches?

    asked by Angel on September 15, 2014
  4. Math

    Which describes the collection of all points in the same plane that are 8 and 1/2 inches from Point T? circle T with radius 8 and 1/ 2 inches circle T with diameter 8 and 1/2 inches circle T with radius 17 inches a sphere with

    asked by Plz Halp on August 8, 2019
  5. MAth

    A sphere has a surface area of 28.26 in2. Find the diameter in inches, of the sphere. Use PI Question 2 What is the surface area, in square inches, of a sphere with radius 3.5 in.? Use Pi and round your answer to the nearest

    asked by Jessica on July 8, 2012
  6. physics

    A metal sphere of radius 5.00 cm is initially uncharged. How many electrons would have to be placed on the sphere to produce an electric field of magnitude 1.59 105 N/C at a point 7.98 cm from the center of the sphere?

    asked by Allie on September 12, 2012
  7. Math and Society

    Which solid has the greatest volume? a)A right cylindrical cylinder with a radius of 4 inches; b)A cube with a side of length of 4 inches; or c) a sphere with a radius of 4 inches?

    asked by Maryanne on May 5, 2012
  8. 10th grade

    The volume of a small sphere is 36 pie cm cubed. The volume of a large sphere is 288 cm cubed and its radius is 6 cm. What is the similarity ratio of the radii of the two spheres? What is the measurement of the small sphere's

    asked by renee on February 23, 2010
  9. physics

    Two solid spheres A and B are made from the same material. The mass of sphere B is eight times that of sphere A. If the radius of sphere A is 7.50 cm, what is the radius of sphere B? [Volume of a sphere of radius r is given by V =

    asked by Mandy on January 19, 2010
  10. college physics

    Two solid spheres A and B are made from the same material. The mass of sphere B is eight times that of sphere A. If the radius of sphere A is 7.50 cm, what is the radius of sphere B? [Volume of a sphere of radius r is given by V =

    asked by Mandy on January 19, 2010

More Similar Questions