Q. 25.0( 1 Vote )
The radius of a s
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
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.
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