Question

The larger and smaller diameter of a cone is 35 m and 15 m. The slant height of the cone is 210 m. What is the surface area of a frustum of cone?
(Use $\pi$ = 22/7).

• A. 83,228.57 m${}^2$
• B. 82,228.57 m${}^2$
• C. 84,228.57 m${}^2$
• D. 81,228.57 m${}^2$

Answer 1

Answer: (C)

84,228.57 m${}^2$

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

Diameter = radius/2

Radius, R = 70 m, r = 30 m, slant height, s = 210 m

SA = $\pi$(70 + 30)210 + $\pi$30${}^2$ + $\pi$70${}^2$

= $\pi$(100)210 + 900$\pi$ + 4900$\pi$

= 22/7 $\times$ (21000 + 900 + 4900)

= 22/7 $\times$ 26,800

= 84,228.57 m${}^2$