Question

The total surface area of a frustum cone is 1,200 m${}^2$. The area of larger and smaller circle is 120 and 100 m${}^2$. Find the curved surface area of a cone.

• A. 980 m${}^2$
• B. 970 m${}^2$
• C. 950 m${}^2$
• D. 960 m${}^2$

Answer 1

The correct option is A 980 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${}^2$ $\Rightarrow$ 1,200 m${}^2$

Smaller circle area = $\pi$r${}^2$ $\Rightarrow$ 100 m${}^2$

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

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

1,200 = Curved surface area + 100 + 120

$1,200-100-120=$ Curved surface area

Curved surface area of a frustum cone = 980 m${}^2$