Name: Parts of a Cuboid
Uploaded: 2019-07-19
Duration: 5 min 14 s
Description: Take this quick lesson on learning everything you'll need to know about cuboids and their faces, edges and vertices. Check out this short video!

Question

The internal and external diameters of a hollow hemispherical shell are

6 cm

and

10 cm

respectively. If it is melted and recast into a solid cylinder of diameter

14 cm

, find the height of the cylinder.

Accepted Answer

The internal and external diameters of a hollow hemispherical shell are $d = 6 cm$ and $D = 10 cm$ respectively

The internal and external radii of the hollow hemispherical shell are $r = \frac{6}{2} = 3 cm$ and $R = \frac{10}{2} = 5 cm$ respectively.

So, the volume of the hollow hemispherical shell $= \frac{2}{3} π (R^{3} - r^{3}) = \frac{2}{3} π (5^{3} - 3^{3}) {cm}^{3} = \frac{2}{3} π (125 - 27) {cm}^{3} = \frac{196}{3} π {cm}^{3}$

Given that, the hollow hemispherical shell is melted and recast into a solid cylinder.

The diameter of the solid cylinder, $D' = 14 cm$

The diameter of the solid cylinder, $r' = \frac{14}{2} = 7 cm$

Let, the height of the solid cylinder is $h cm$

So, the volume of the solid cylinder $= π {(r')}^{2} h = π {(7)}^{2} h {cm}^{3}$

Since the hollow hemispherical shell is melted and recast into the solid cylinder,

So, the volume of the solid cylinder $=$ the volume of the hollow hemispherical shell

$∴ π {(7)}^{2} h = \frac{196}{3} π \Rightarrow h = \frac{196 π}{3 \times 49 π} = \frac{4}{3} cm = 1.33 cm (approx)$

Hence, the height of the cylinder is $1.33 cm (approx)$ .

The internal and external diameters of a hollow hemispherical shell are $6 cm$ and $10 cm$ respectively. If it is melted and recast into a solid cylinder of diameter $14 cm$ , find the height of the cylinder.

Important Questions on Surface Areas & Volumes

Learn and Prepare for any exam you want !

The internal and external diameters of a hollow hemispherical shell are 6 cm and 10 cm respectively. If it is melted and recast into a solid cylinder of diameter 14 cm, find the height of the cylinder.

Important Questions on Surface Areas & Volumes

Learn and Prepare for any exam you want !

The internal and external diameters of a hollow hemispherical shell are $6 cm$ and $10 cm$ respectively. If it is melted and recast into a solid cylinder of diameter $14 cm$ , find the height of the cylinder.