Question

The smaller diameter of a frustum cone is thrice the larger radius which is 4 in. The slant height of the cone is 13 in. What is the surface area? (Use $\pi$ = 3).

• A. 2,768 in${}^2$
• B. 2,868 in${}^2$
• C. 2,668 in${}^2$
• D. 2,568 in${}^2$

Answer 1

The correct option is B 2,868 in${}^2$

Surface area of a frustum of cone = $\pi$(r + R)s + $\pi$r${}^2$ + $\pi$R${}^2$

Larger radius = 4 in

Smaller diameter = 3$\times$ larger radius $\Rightarrow$ 3 $\times$ 4 =12 in

Smaller radius = 24 in

s = 13 in

SA = $\pi$(24 + 4)13 + $\pi$24${}^2$ + $\pi$4${}^2$

= $\pi$(28)13 + 576$\pi$ + 16$\pi$

= 3 $\times$ (364 + 576 + 16)

= 3 $\times$ 956

= 2,868 in${}^2$