Question

A team of engineers must design a fuel tank in the shape of a cone (excluding the base) is given by the formula S=Pi x square root of (r^2 + h^2). Find the radius of a cone with a height of 21 meters and a surface area of 155 meters squared. Round your answer to the nearest tenth if necessary.

Answer 1

The radius of cone is 44.6 meters.

Explanation:

Consider the provided information.

The shape of a cone (excluding the base) is given by the formula S=Pi x square root of (r^2 + h^2).

This can be written as:

`S=\pi * √(r^2+h^2)`

We need to find the radius of a cone with a height of 21 meters and a surface area of 155 meters squared.

Substitute the respective values in the above formula.

`155=\pi * √(r^2+21^2)`

`(155)/(\pi)=√(r^2+21^2)`

`49.32=√(r^2+441)`

`2432=r^2+441`

`1991=r^2`

`r=44.6\ approximately`

Hence, the radius of cone is 44.6 meters.

Answer 2

To answer the given question, substitute the values given to the equation,
S = π x sqrt(r² + h²)

155 m = π x sqrt (r² + (21 m)²))

r = 44.65 m
Therefore, the radius of the cone is approximately 44.65 m.