Question

The larger diameter of a frustum cone is double the smaller diameter which is 6 cm. The slant height of the cone is 20 cm. What is the surface area? (Use $\pi$ = 3.14).

• A. 4,721.6 cm${}^2$
• B. 4,821.6 cm${}^2$
• C. 4,621.6 cm${}^2$
• D. 4,521.6 cm${}^2$

Answer 1

The correct option is D 4,521.6 cm${}^2$

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

Larger diameter = 2 $\times$ smaller diameter $\Rightarrow$ 2 $\times$ 6 =12 cm

Smaller diameter = 6cm

Diameter = radius/2

Radius, R = 24 cm, r = 12 cm

s = 20 cm

SA = $\pi$(12 + 24)20 + $\pi$12${}^2$ + $\pi$24${}^2$

= $\pi$(36)20 + 144$\pi$ + 576$\pi$

= 3.14 $\times$ (720+ 144 + 576)

= 3.14 $\times$ 1,440

= 4,521.6 cm${}^2$