Question

A semi-circular sheet of metal of diameter 28cm and is bent into an open conical cup. Find depth and capacity of cup.

• A.
  663.346 cm${}^3$
• B.
  435.098 cm${}^3$
• C.
  622.365 cm${}^3$
• D.
  755.456 cm${}^3$

Answer 1

The correct option is C

622.365 cm${}^3$


Circumference of circular base of cone = Circumference of semi-circular sheet
$\Rightarrow 2\pi r=\pi R$
$\Rightarrow r=\frac{R}{2}=\frac{14}{2}=7cm$
l = 14cm, r = 7cm
l = $\sqrt{r^2+h^2}$
$\Rightarrow \sqrt{(7{)}^2+(h{)}^2}=14$
$\Rightarrow 49+h^2=196$
$\Rightarrow h^2=147$
$h=7\sqrt{3}$cm

The capacity of conical cup =$\frac{1}{3}\pi r^{2}h$
$=\frac{1}{3}\times \frac{22}{7}\times 7\times 7\times 7\sqrt{3}$
$=\frac{22\times 49\times 1.732}{3}=\frac{1867.096}{3}$
= 622.365 cm${}^3$