Question

The curved surface area of a frustum cone is 250 mm${}^2$. The smaller circle area is 35 mm${}^2$. The total surface area is 450 mm${}^2$. Find the larger circle area of a cone.

• A. 155 mm${}^2$
• B. 165 mm${}^2$
• C. 175 mm${}^2$
• D. 185 mm${}^2$

Answer 1

The correct option is B 165 mm${}^2$

Curved surface area of a frustum cone = $\pi$(r + R)s $\Rightarrow$ 250 mm${}^2$

Total surface area of a frustum of cone = $\pi$(r + R)s + $\pi$r${}^2$ + $\pi$R${}^2$ $\Rightarrow$ 450 mm${}^2$

Smaller circle area = $\pi$r${}^2$ $\Rightarrow$ 35 mm${}^2$

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

Therefore,

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

$450=250$+ Area of larger circle + 35

$450-250-35=$Area of larger circle

Area of larger circle of a frustum cone = 165 mm${}^2$