Question

if caramel is put onto a sphere-shaped apple such that the surface area increase at a rate of 10 cm2/min, find the rate at which the diameter increases when the diameter is 15cm

Answer 1

The diameter will increase at a rate of 1/30π cm/min

Explanation:

Here we want to calculate the rate at which the diameter will increase

Mathematically, the area of a sphere is given as;

A = 4πr^2

But r = d/2

so A = 4 * π * d/2 * d/2 = πd^2

dA/d(d) = 2πd

Thus dd/dA = 1/2πd = 1/2 * π * 15 = 1/30π

Given dA/dt = 10

Mathematically;

d(d)/dt = d(d)/dA * dA/dt

dd/dt = 1/30π * 10 = 10/30π = 1/3π cm/min