Math Calculus
posted by Megan .
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 :)

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 
Thank you soo muccchh

sorry actually i got that part which is part a. What I need is part (b). Find the delta(v)
Respond to this Question
Similar Questions

Geometry
Can someone please check these for me. I have to leave answers in Pi. Find the Volume of a right cone with radius 6 height 10 V=1/3 pi r squared*h =1/3pi (6)^2(10) =1/3(360)pi =120pi Find the volume of a sphere with radius 3cm V=4/3 … 
Math
Ryan estimates the measurement of the volume of a popcorn container to be 282 cubic inches. The actual volume of the popcorn container is 289 cubic inches. What is the relative error of ryan's measurement to the nearest thousandth? 
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? 
calculus
3. The radius r of a sphere is increasing at a constant rate of 0.04 centimeters per second. (Note: The volume of a sphere with radius r is v=4/3pir^3 ). a. At the time when the radius of the sphere is 10 cm, what is the rate of increase … 
Calculus
4. At time t, t>0, the volume of a sphere is increasing at a rate proportional to the reciprocal of its radius. At t = 0, the radius of the sphere is 1 and at t = 15 the radius is 2. a. Find the radius of the sphere as a function … 
PreAlgebra
For numbers 1–3, find the indicated measurement of the figure described. Use 3.14 for (pi) and round to the nearest whole number. 1) Find the surface area of a sphere with a radius of 8 cm. a. 268 cm2 b. 804 cm2 c. 2,144 cm2 d. 201 … 
math
The volume of a sphere is given by V=4*r^3/3, where r is the radius,compute the radius of a sphere having a volume 40 percent greater than that of a sphere of radius 4 ft? 
Calculus
An error in the measurement of the radius of a circle results in an error in the computation of its area. Find and interpret the sensitivity of area (a) of a circle to the measurement of radius, r, when the radius r=2 meters. 
math
3.A rectangular prism has a width of 92ft and a volume of 240ft.Find the volume of a similar prism with a width of 23ft.Round to the nearest tenth, if necessary. 4.A pyramid a height of 5in. and a surface area of 90in^2.Find the surface … 
Calculus
Imagine slicing through a sphere with a plane (sheet of paper). the smaller piece produced is called a radius of the sphere. Its volume is V=(pi)h^2(3rh)/3, where r is the radius of the sphere and h is the thickness of the cap. find …