Question

A right cone has radius 3 ft and slant height 7 ft. The radius and slant height are both doubled. Which of the following correctly describes the effect on the surface area?

The surface area is multiplied by 4.
The surface area is multiplied by 2.
The surface area is multiplied by 1/4.
The surface area is multiplied by 1/2.

Answer 1

$\bf \textit{surface area of a cone}\\\\ SA=\pi r s+\pi r^2~~ \begin{cases} r=radius\\ s=slant~height\\[-0.5em] \hrulefill\\ r=\stackrel{doubled}{2r}\\ s=\stackrel{doubled}{2s} \end{cases} \\\\\\ SA=\pi (2r)(2s)+\pi (2r)^2\implies SA=4\pi rs+\pi (2^2r^2) \\\\\\ SA=4\pi rs+4\pi r^2\implies SA=4\left(\pi rs+\pi r^2 \right)\leftarrow \begin{array}{llll} \textit{original SA}\\ \textit{is multiplied by 4} \end{array}$