Question

The curved surface area of a frustum cone is 25$\pi$ mm${}^2$. The larger circle area is 12$\pi$ mm${}^2$. The total surface area is $350\pi$ mm${}^2$. Find the smaller circle area of a cone.

• A. 313 mm${}^2$
• B. 323$\pi$ mm${}^2$
• C. 333$\pi$ mm${}^2$
• D. 313$\pi$ mm${}^2$

Answer 1

Answer: (D)

313$\pi$ mm${}^2$

Curved surface area of a frustum cone = $\pi$(r + R)s $\Rightarrow$ 25$\pi$ mm${}^2$

Total surface area of a frustum of cone = $\pi$(r + R)s+ $\pi$r${}^2$ + $\pi$R${}^2$ $\Rightarrow$ 350$\pi$ mm${}^2$

Larger circle area = $\pi$R${}^2$ $\Rightarrow$ 12$\pi$ mm${}^2$

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

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

350$\pi$ = 25$\pi$ + Area of smaller circle + 12$\pi$

350$\pi$ - 25$\pi$- 12$\pi$ = Area of smaller circle

Area of smaller circle of a frustum cone = 313$\pi$ mm${}^2$