A solid hemisphere of wax of radius $12 c m$ is melted and made into a cylinder of its base radius $6 c m$ . Calculate the height (in $c m$ ) of the cylinder.

Open in App

Solution

Volume of hemisphere $=$ Volume of cylinder
$\frac{2}{3} π r_{1}^{3} = π r_{2}^{2} h$
$\frac{2}{3} \times 12 \times 12 \times 12 = 6 \times 6 \times h$
$32 = h$
$∴ h = 32 c m$

Suggest Corrections

Similar questions

Q. A solid cylinder of diameter 12 cm and height 15 cm is melted and recast into toys in the shape of a right circular cone mounted on a hemisphere of radius 3 cm. If the height of the toy is 12 cm, find the number of toys so formed.

Q. A solid metallic cylinder of radius

12 c m

and height

175 c m

is melted and moulded into another solid cylinder of height

63 c m

. What is the radius of the new cylinder?

A cylinder with base radius 8 cm and height 2 cm is melted to form a cone of height 6 cm. Calculate the radius of the base of the cone.

A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder (in cm).

___

The base radius of an iron cylinder is 14 cm and its height is 28 cm. It is melted and recast into a cylinder of base radius 20 cm. What is the height of this cylinder of base radius 20 cm?

Join BYJU'S Learning Program

A solid hemisphere of wax of radius 12 cm is melted and made into a cylinder of its base radius 6 cm. Calculate the height (in cm) of the cylinder.

Volume of hemisphere = Volume of cylinder23πr31=πr22h23×12×12×12=6×6×h32=h∴h=32 cm

A solid hemisphere of wax of radius $12 c m$ is melted and made into a cylinder of its base radius $6 c m$ . Calculate the height (in $c m$ ) of the cylinder.

Volume of hemisphere $=$ Volume of cylinder
$\frac{2}{3} π r_{1}^{3} = π r_{2}^{2} h$
$\frac{2}{3} \times 12 \times 12 \times 12 = 6 \times 6 \times h$
$32 = h$
$∴ h = 32 c m$