Question

A right triangle with sides 6 cm, 8 cm and 10 cm is revolved about the side 8 cm. Find the

volume and curved surface of the solid so formed.

Answer 1

The volume and the curved surface area of the solid formed is
`301.71\ \text{cm}^3` and
`188.57\ \text{cm}^2` respectively.

Explanation:

Given that,

A right triangle with sides 6 cm, 8 cm and 10 cm is revolved about the side 8 cm.

As the triangle is revolved at 8 cm it forms a cone of height 8 cm and radius 6cm.

Height, h = 8 cm

Radius, r = 6 cm

The volume of the solid formed is given by :

`V=(1)/(3)\pi r^2 h\\\\=(1)/(3)* (22)/(7)* 8^2* 8\\\\=301.71\ \text{cm}^3`

The curved surface of the solid formed is :

`A=\pi rl`

l is slant height

`A=\pi r* √(h^2+r^2) \\\\A=(22)/(7)* 6* √(8^2+6^2) \\\\=188.57\ \text{cm}^2`

Hence, the volume and the curved surface area of the solid formed is
`301.71\ \text{cm}^3` and
`188.57\ \text{cm}^2` respectively.