Question

The volume of a solid hemisphere is $ 1152\pi c{m^3} $ Find its curved surface area.

Answer 1

Hint: Here we are given the volume of the solid hemisphere and by using the formula will find the radius of the solid hemisphere and then by getting the value of radius will find the curved surface area.

Complete step-by-step answer:
Volume of the solid hemisphere can be expressed as $ V = \dfrac{2}{3}\pi {r^3} $ …. (A)
Given that the volume of the solid hemisphere is $ 1152\pi c{m^3} $ …. (B)
From the equations (A) and (B)
 $ 1152\pi = \dfrac{2}{3}\pi {r^3} $
Common factors from both the sides of the equation cancel each other and therefore remove from both the sides of the equation.
 $ 1152 = \dfrac{2}{3}{r^3} $
Term in denominator if moved to the opposite side then it is multiplied with the numerator.
 $ \dfrac{{1152 \times 3}}{2} = {r^3} $
The above expression can be re-written as –
 $ {r^3} = 576 \times 3 $
Simplify the above expression multiplying the terms on the right hand side of the equation.
 $ {r^3} = 1728 $
Find the cube-root on both the sides of the above equation.
 $ r = 12cm $ …. (C)
The curved surface area of the hemisphere is given by, $ A = 2\pi {r^2} $
By using the equation (C)
 $ A = 2(\pi ){(12)^2} $
Simplify the above expression –
 $ A = 288\pi c{m^2} $
Hence, the required answer is – the curved surface of the hemisphere is $ 288\pi c{m^2} $
So, the correct answer is “$ 288\pi c{m^2} $”.

Note: Remember all the formulas for the volume and area for the closed and open figures. Know the difference between the volume and the areas of the figures. Volume is measured in cubic units and the area is measured in the square units.