Question

A solid cube of side 8 cm was melted to form a solid circular cone. The base radius of the cone is 4 cm. Calculate, correct to one decimal place, the height of the cone. [Take π = 22/7 ]​

Answer 1

• 34.1 cm

Explanation:

A solid cube of side 8 cm was melted to form a solid circular cone.

Side of cube = 8 cm .

• Volume of cube = a³

where a is side of the cube.

Volume of cube = (8)³

Volume of cube = 8 × 8 × 8 = 512 cm³

The base radius of the cone is 4 cm.

Since the solid cube is melted to form a solid circular cone, but the volume will remains the same.

Volume of cone = Volume of cylinder = 512 cm³

Formula to calculate the volume of cone :

`\rm Volume (cone) = (1)/(3) \pi { r}^(2) h`

Plugging in the values of radius and volume

`512 = (1)/(3) * (22)/(7) * {(4)}^(2) * h \\ \\ 512 = (22)/(21) * 16 * h \\ \\ 512 = (352)/(21) * h \\ \\ 512 = 16.76 * h \\ \\ h = (572)/(16.76) \\ \\ h \approx 34.1`

`\therefore` The height of the cone is 34.1 cm