Name: Area of Quadrilateral Using Heron's Formula
Uploaded: 2019-07-19
Duration: 10 min 24 s
Description: Did you know that the area of a quadrilateral can be calculated by dividing the quadrilateral into two triangles and using Heron's formula? Let's watch this...

Question

A solid is in the form of a cone surmounted on a hemisphere of the same radius. If the height of the cone is

24 cm

and radius of the hemisphere is

7 cm

, find the volume and surface area of the solid.

Accepted Answer

Given: Height of the cone $= 24 cm$ , Radius of cone and hemisphere is $7 cm$ .

The volume of the solid $=$ Volume of cone $+$ Volume of the hemisphere

$= \frac{1}{3} {πr}^{2} h + \frac{2}{3} {πr}^{3}$

$= \frac{1}{3} {πr}^{2} (h + 2 r)$

$= \frac{1}{3} \times \frac{22}{7} \times 7^{2} (24 + 2 \times 7)$

$= \frac{1}{3} \times \frac{22}{7} \times 7 \times 7 \times 38$

$= \frac{5852}{3} {cm}^{3}$

$= 1950 \frac{2}{3} {cm}^{3}$

The surface area of the solid $= C S A$ of cone $7 cm$ of hemisphere

$= πrl + 2 {πr}^{2}$

$= πr \sqrt{h^{2} + r^{2}} + 2 {πr}^{2}$

$= \frac{22}{7} \times 7 (\sqrt{24^{2} + 7^{2}}) + 2 \times \frac{22}{7} 7 \times 7$

$= \frac{22}{7} \times 7 [(\sqrt{576 + 49}) + 2 \times 7]$

$= 22 [(\sqrt{625}) + 14]$

$= 22 [25 + 14]$

$= 22 \times 39$

$= 858 {cm}^{2}$

Therefore, the volume of the solid is $1950 \frac{2}{3} {cm}^{3}$ and surface area is $858 {cm}^{2}$ .

A solid is in the form of a cone surmounted on a hemisphere of the same radius. If the height of the cone is $24 cm$ and radius of the hemisphere is $7 cm$ , find the volume and surface area of the solid.

Important Questions on Mensuration

Learn and Prepare for any exam you want !

A solid is in the form of a cone surmounted on a hemisphere of the same radius. If the height of the cone is 24 cm and radius of the hemisphere is 7 cm, find the volume and surface area of the solid.

Important Questions on Mensuration

Learn and Prepare for any exam you want !

A solid is in the form of a cone surmounted on a hemisphere of the same radius. If the height of the cone is $24 cm$ and radius of the hemisphere is $7 cm$ , find the volume and surface area of the solid.