Question

The total surface area of a frustum cone is 311.56 m${}^2$. The area of larger and smaller circle is 12 and 8.4 m${}^2$. Find the curved surface area of a cone.

• A. 191.16 m${}^2$
• B. 391.16 m${}^2$
• C. 491.16 m${}^2$
• D. 291.16 m${}^2$

Answer 1

The correct option is D 291.16 m${}^2$

Curved surface area of a frustum cone = $\pi$(r + R)s $\Rightarrow$ ?

Total surface area of a frustum of cone = $\pi$(r + R)s+ $\pi$r${}^2$ + $\pi$R${}^2$ $\Rightarrow$ 311.56 m${}^2$

Smaller circle area = $\pi$r${}^2$ $\Rightarrow$ 8.4 m${}^2$

Larger circle area = $\pi$R${}^2$ => 12 m${}^2$

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

311.56 = Curved surface area + 8.4 + 12

$311.56-8.4-12=$Curved surface area

Curved surface area of a frustum cone = 291.16 m${}^2$