Question

A right angled triangle of which the sides containing the right angle are 6.3 cm and 10 cm in length, is made to turn round on the longer side. Find the volume of the solid, thus generated. Also, find its curved surface area.

Answer 1

When you rotate a right triangle about one of its sides containing the right angle the solid so formed will be a cone.

Here the right triangle has sides 6.3 cm and 10 cm and it is said that the right triangle is rotated about its longer side. So here it will be the side of 10 cm length.

So, the height of the cone thus formed will be ‘h’ = 10 cm, and the radius ‘r’ = 6.3 cm.

The formula of the volume of a cone with base radius ‘r’ and vertical height ‘h’ is given as

Volume of cone =

Substituting the values of r = 6.3 cm and h = 10 cm in the above equation and using

Volume =

=

= 415.8

Hence the volume of the given cone with the specified dimensions is

The formula of the curved surface area of a cone with base radius ‘r’ and slant height ‘l’ is given as

Curved Surface Area = πrl

To find the slant height ‘l’ to be used in the formula for Curved Surface Area we use the following relation

Slant height, l =

=

=

=

Hence the slant height l of the cone is cm.

Now, substituting the values of r = 6.3 cm and slant height l = cm and using in the formula of C.S.A,

We get Curved Surface Area =

= 233.8

Hence the curved surface area of the so formed cone is