Question

The curved surface area of a frustum cone is 250 m${}^2$. The larger circle area is 120 m${}^2$. The total surface area is 1000 m${}^2$. Find the smaller circle area of a cone.

• A. 630 m${}^2$
• B. 620 m${}^2$
• C. 610 m${}^2$
• D. 600 m${}^2$

Answer 1

The correct option is A 630 m${}^2$

Curved surface area of a frustum cone $=\pi$(r + R)s $\Rightarrow$ 250 m${}^2$
Surface area of a frustum of cone = $\pi$(r + R)s + $\pi$r${}^2$ + $\pi$R${}^2$ $\Rightarrow$ 1000 m${}^2$

Larger circle area = $\pi$R${}^2$ $\Rightarrow$ 120 m${}^2$

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

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

100 = 250 + Area of smaller circle + 120

1000 = 250
120 = Area of smaller circle

Area of smaller circle of a frustum cone = 630 m${}^2$