Q. 25.0( 1 Vote )

# The radius of a s

Answer :

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 cm^{3}.

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