Question

Find the height and slant height of the cone. Round your answers to the nearest whole number.

Answer 1

Height = 4 cm and slant height = 5 cm

Explanation:

Given that,

The surface area of the cone, A = 75.4 cm²

Radius, r = 3 cm

The surface area of the cone is given by the formula as follows :

`A=\pi r^2+\pi rl`

Put all the values,

`75.4=3.14* 3^2+3.14* 3* l\\\\75.4=28.26+9.42l\\\\75.4-28.26=9.42l\\\\47.14=9.42l\\\\l=(47.14)/(9.42)\\\\l=5\ cm`

Also,

`l^2=r^2+h^2\\\\h=√(l^2-r^2)\\\\h=√(5^2-3^2)\\\\h=4\ cm`

Hence, the height of the cone is 4 cm and the slant height is 5 cm.