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+√(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*7(7+√(5^2+7^2)) \\ A=7\pi(7+√(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=(109.216\pi)/(27.305\pi) \\ ratio\approx(4)/(1) \end{gathered}`

Therefore, the ratio is 4:1.

OPTION B is the correct option.