Respuesta :
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.
[tex]\dfrac{\text{Area of cone}}{\text{Area of new cone}}=\dfrac{\text{Radius of cone}^2}{\text{Radius of new cone}^2}[/tex]
Let the surface area of new cone be A and r be the radius of original cone
[tex]\dfrac{32}{A}=\dfrac{(r)^2}{(3r)^2}[/tex]
[tex]\dfrac{32}{A}=\dfrac{r^2}{9r^2}[/tex]
[tex]\dfrac{32}{A}=\dfrac{1}{9}[/tex]
By cross multiplication, we get
[tex]32\times 9=1\times A[/tex]
[tex]288=A[/tex]
The surface area of the new cone is 288 sq. cm.
Therefore, the correct option is C.
