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

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.

Answer 2

Answer:

The radius of cone is 44.6 meters.

Step-by-step 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:

$S=\pi \times \sqrt{r^2+h^2}$

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.

$155=\pi \times \sqrt{r^2+21^2}$

$\frac{155}{\pi}=\sqrt{r^2+21^2}$

$49.32=\sqrt{r^2+441}$

$2432=r^2+441$

$1991=r^2$

$r=44.6\ approximately$

Hence, the radius of cone is 44.6 meters.