Question

The curved surface area of a frustum cone is 2.34 cm${}^2$. The larger circle area is 12.5 cm${}^2$. The total surface area is 25.8 cm${}^2$. Find the smaller circle area of a cone.

• A. 12.96 cm
• B. 11.96 cm
• C. 10.96 cm
• D. 9.96 cm

Answer 1

The correct option is C 10.96 cm

Curved surface area of a frustum cone = $\pi$(r + R)s $\Rightarrow$ 2.34 cm${}^2$

Total surface area of a frustum of cone $=\pi$ (r + R)s + $\pi r^2$ + $\pi R^2$$\Rightarrow$ 25.8$c{m}^2$

Larger circle area = $\pi$R${}^2$ $\Rightarrow$ 12.5 cm${}^2$

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

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

25.8 = 2.34 +Area of smaller circle + 12.5

$25.8-2.34-12.5=$Area of smaller circle

Area of smaller circle of a frustum cone = 10.96 cm${}^2$