Question

What is the ratio for the surface areas of the cones shown below, given thatthey are similar and that the ratio of their radii and altitudes is 2:1?OA. 8:1B. 4:1OC. 1:4OD. 1:87-2.5-3.5-

Answer 1

The formula to calculate the surface area of a cone is given to be:

$A=\pi r(r+\sqrt{h^2+r^2})$

where r is the radius and h is the perpendicular height.

The surface area of the big cone is calculated as follows:

$\begin{gathered} h=5 \\ r=7 \\ \therefore \\ A=\pi\times7(7+\sqrt{5^2+7^2}) \\ A=7\pi(7+\sqrt{74}) \\ A=109.216\pi \end{gathered}$

The surface area of the smaller cone is:

$\begin{gathered} h=2.5 \\ r=3.5 \\ \therefore \\ A=27.305\pi \end{gathered}$

Hence, the ratio is calculated as follows:

$\begin{gathered} ratio=\frac{109.216\pi}{27.305\pi} \\ ratio\approx\frac{4}{1} \end{gathered}$

Therefore, the ratio is 4:1.

OPTION B is the correct option.