Radius of the circle is 21 m and the area of the circle is 54 m2 less than the sum of the lateral surface area

Radius of the circle is 21 m and the area of the circle is 54 m2 less than the sum of the lateral surface area and the total surface area of the cube. Find the volume of the cube.

a) 729 m3

b) 2197 m3

c) 1728 m3

d) 1000 m3

e) None of these

Sol:

Area of the circle = 22/7 * 21 * 21 = 1386 m2

Let the side of the cube be a

4a² + 6a² = 1386 + 54

10a² = 1440

a² = 144

a = 12 m

Volume of the cube = 12 * 12 * 12 = 1728 m3