passpadi

2001

Mathematics

JAMB

Find the rate of change of the volume, V of a sphere with respect to its radius, r when r = 1.

A.

12π

B.

C.

24π

D.

Correct Answer:

Explanation

Volume of sphere, V = 4/3 x πr3 Rate of change of V = dv/dr Thus if V = 4/3 x πr3, => dv/dr = 4πr2 At r = 1, Rate = 4 x π x 1 = 4π

Volume of sphere, V = 4/3 x πr3 Rate of change of V = dv/dr Thus if V = 4/3 x πr3, => dv/dr = 4πr2 At r = 1, Rate = 4 x π x 1 = 4π
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