Question

the largest cone is curved out from one face of solid cube of side 21 find the volume of the remaining solid

Answer 1

Largest possible diameter of the cone = length of the cube

⇒ Diameter = 21 cm

⇒ Radius = 21 ÷ 2 = 10.5 cm

Largest possible height of the cone = length of the cube

⇒ height = 21 cm

Find the volume of the cone:

Volume = 1/3 πr²h

Volume = 1/3 π(10.5)²(21) = 2425.5 cm³

Find the volume of the cube:

Volume = length³

Volume = 21³

Volume = 9261 cm³

Find the remaining volume:

Remaining volume = 9261 - 2425.5 = 6835.5 cm³

Answer: 6835.5 cm³