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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.

Respuesta :

meerkat18
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:

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:

[tex]S=\pi \times \sqrt{r^2+h^2}[/tex]

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.

[tex]155=\pi \times \sqrt{r^2+21^2}[/tex]

[tex]\frac{155}{\pi}=\sqrt{r^2+21^2}[/tex]

[tex]49.32=\sqrt{r^2+441}[/tex]

[tex]2432=r^2+441[/tex]

[tex]1991=r^2[/tex]

[tex]r=44.6\ approximately[/tex]

Hence, the radius of cone is 44.6 meters.

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