Question

The radius of the outer circumference of a cylindrical ring is $12cm$ and the diameter of the cross-section is $1.5cm$. Then, the volume of circular ring is

• A. $22.5c{m}^3$
• B. $125c{m}^3$
• C. $226c{m}^3$
• D. $1250c{m}^3$

Answer 1

The correct option is B $125c{m}^3$

Let ABCD be a cylindrical ring whose outer radius $=R=12cm$.
$\Rightarrow$ Outer diameter $=D=24cm$

Diameter of cross - section $CD = 1.5 cm$
Area of cross - section $CD=\frac{\pi }{4}\left(CD\right)=\frac{\pi }{4}(1.5{)}^{2}c{m}^2$
$\therefore$ Volume of circular ring $=Al$
where, $A=\frac{\pi }{4}(1.5{)}^{2}c{m}^2$
$l=\pi (D-W)=\pi (24-1.5)$$=\pi \times 22.5cm$
Volume$=\frac{\pi }{4}\times (1.5{)}^2\times \pi \times 22.5$$=125c{m}^3$