Question

A conical cavity of maximum volume is carved out from a wooden solid hemisphere of radius 10 cm. Curved surface area of the cavity carved out is (Use π = 3.14)

Options

• `314 sqrt(2)  cm^2`

• 314 cm²

• `3140/3 cm^2`

• `3140 sqrt(2)  cm^2`

Answer 1

`bb(314 sqrt(2)  cm^2)`

Explanation:

Given: Radius of hemisphere R = 10 cm.

For maximum volume for the cone:

Radius r = R = 10 cm

Height h = R = 10 cm

First, we find the slant height (`l`):

`l = sqrt(r^2 + h^2)`

= `sqrt(10^2 + 10^2)`

= `sqrt(100 + 100)`

= `sqrt(200)`

= `10sqrt(2)  cm`

Now, calculate the Curved Surface Area:

CSA = `π xx 10 xx 10sqrt(2)`

CSA = `3.14 xx 100sqrt(2)`

CSA = `314sqrt(2)  cm^2`

The curved surface area of the cavity is `314sqrt(2)  cm^2`.