The radius of a sphere shrinks from 10 to 9.8 cm. Find approximately the decrease in its volume.

Given the radius of a sphere changes from 10 cm to 9.8 cm.

Let x be the radius of the sphere and Δx be the change in the value of x.

Hence, we have x = 10 and x + Δx = 9.8

⇒ 10 + Δx = 9.8

⇒ Δx = 9.8 – 10

∴ Δx = –0.2

The volume of a sphere of radius x is given by

On differentiating V with respect to x, we get

We know

When x = 10, we have.

Recall that if y = f(x) and Δx is a small increment in x, then the corresponding increment in y, Δy = f(x + Δx) – f(x), is approximately given as

Here, and Δx = –0.2

⇒ ΔV = (400π)(–0.2)

∴ ΔV = –80π

Thus, the approximate decrease in the volume of the sphere is 80π cm³.