Question

The curved surface area of a frustum cone is 34.7 in${}^2$. The smaller circle area is 15.8 in${}^2$. The total surface area is 70.5 in${}^2$. Find the larger circle area of a cone.

• A. 10 in${}^2$
• B. 30 in${}^2$
• C. 40 in${}^2$
• D. 20 in${}^2$

Answer 1

The correct option is D 20 in${}^2$

Curved surface area of a frustum cone = $\pi$(r + R)s $\Rightarrow$ 34.7 in${}^2$

Total surface area of a frustum of cone = $\pi$(r + R)s + $\pi$r${}^2$ + $\pi$R${}^2$ $\Rightarrow$ 70.5 in${}^2$

Smaller circle area = $\pi$r${}^2$ $\Rightarrow$ 15.8 in

Larger circle area = $\pi$R${}^2$ $\Rightarrow$ ?

Therefore,
SA = $\pi$(r + R)s + $\pi$r${}^2$ + $\pi$R${}^2$

70.5 = 34.7 + Area of larger circle + 15.8

70.5 - 34.7 - 15.8 = Area of larger circle

Area of larger circle of a frustum cone = 20 in${}^2$