Question

The total surface area of a frustum cone is 3,250 cm${}^2$. The area of larger and smaller circle is 48 and 36 cm${}^2$. Find the curved surface area of a cone.

• A. 3,166 cm${}^2$
• B. 3,266 cm${}^2$
• C. 3,366 cm${}^2$
• D. 3,466 cm${}^2$

Answer 1

The correct option is A 3,166 cm${}^2$

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${}^2$ $\Rightarrow$ 3,250 cm${}^2$

Smaller circle area = $\pi$r${}^2$ $\Rightarrow$ 36 cm${}^2$

Larger circle area = $\pi$R${}^2$ $\Rightarrow$ 48 cm${}^2$

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

3,250 = Curved surface area + 36 + 48

$3,250-36-48=$Curved surface area

Curved surface area of a frustum cone = 3,166 cm${}^2$