Question

The ratio of total surface area of a solid hemisphere to the square of its radius is ______.

Options

• 2π : 1

• 4π : 1

• 3π : 1

• 1 : 4π

Answer 1

The ratio of total surface area of a solid hemisphere to the square of its radius is 3π : 1.

Explanation:

Curved Surface Area = 2πr²

Curved Surface Area of Hemisphere = `(1/2) 4πr^2 = 2πr^2` 

Base Area of a hemisphere = πr²

Total Surface Area of Hemisphere = 2πr² + πr² = 3πr²

Divide the total surface area by r²

`= (3pir^2)/r^2`

`= 3pi`

Therefore, the ratio of the total surface area of a solid hemisphere to the square of its radius is 3π : 1