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