Question

The radius and height of a cone are in the ratio 7:24. Find the the radius and slant height if the volume of the cone is 154cm cube

Answer 1

Ratio of radius and height of cone=7:24

Let r=7x and h=24x

Volume of the cone=154cm³

1/3πr²h=154cm³

1/3*22/7*7x*7x*24x=154

1176x³=154*3*7/22

x³=154/1176*3*7/22

x³=3234/25872

x³=0.125

x=0.5

Radius =7x=7(0.5)=3.5cm

Height =24x=24(0.5)=12cm

Slant height of cone(l)=√r²+h²

=√3.5²+12²

=√12.25+144

=√156.25

Slant height =12.5cm