Question

A right cone has radius 2 ft and slant height 5 ft. The radius and slant height are both multiplied by 1/4. Which of the following correctly describes the effect on the surface area?

The surface area is multiplied by 8.
The surface area is multiplied by 1/16.
The surface area is multiplied by 16.
The surface area is multiplied by 1/8.

Answer 1

 

k = coefficient of similarity for lengths

k ^ 2 = coefficient of similarity for surfaces

k ^ 3 = coefficient of similarity for volumes

$\displaystyle\bf\\ \text{Coefficient of similarity for lengths}=~k=\frac{1}{4}\\\\\implies~\text{Coefficient of similarity for surfaces}=k^2=\left(\frac{1}{4}\right)^{\b2}=\boxed{\bf\frac{1}{16}}$

⇒  The surface area is multiplied by 1/16