Question

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

Answer 1

Diameter of the circular sheet is $28$cm

Radius$=14$cm

Circumference of semicircular sheet$=14\pi$

Now, the semicircular sheet is bent in to an open conical cup.

Slant height of conical cup$=l=$radius of circular sheet$=14$cm

Circumference of the base of conical cup$=$Circumference of semicircular sheet

$\Rightarrow 2\pi r=14\pi$

$\Rightarrow r=7$cm

Depth of conical cup$=$Height of cone$=\sqrt{l^2-r^2}=\sqrt{{14}^2-7^2}=\sqrt{196-49}=\sqrt{147}=7\sqrt{3}$cm

Capacity of conical cup$=$Volume of cone$=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times \frac{22}{7}\times 7\times 7\times 7\sqrt{3}=\frac{1078\sqrt{3}}{3}{cm}^3$