Question

The surface area of a right circular cone is 32 cm. This cone is enlarged by multiplying both the radius and slant height by 3. What is the surface area of the new cone? A. 35 cm B. 96 cm C. 288 cm D. 192 cm

Answer 1

Answer 288

Explanation:

Answer 2

Given:

The surface area of a right circular cone is 32 sq. cm.

Scale factor for enlargement = 3

To find:

The surface area of the new cone.

Solution:

We know that enlargement of a shape forms a similar shape and area of the similar shapes is proportional to the square of their corresponding sides.

`\frac{\text{Area of cone}}{\text{Area of new cone}}=\frac{\text{Radius of cone}^2}{\text{Radius of new cone}^2}`

Let the surface area of new cone be A and r be the radius of original cone

`(32)/(A)=((r)^2)/((3r)^2)`

`(32)/(A)=(r^2)/(9r^2)`

`(32)/(A)=(1)/(9)`

By cross multiplication, we get

`32* 9=1* A`

`288=A`

The surface area of the new cone is 288 sq. cm.

Therefore, the correct option is C.