Question

Height of a solid cylinder is 10 cm and diameter 8 cm. Two equal conical hole have been made from its both ends. If the diameter of the holes is 6 cm and height 4 cm, find (i) volume of the cylinder, (ii) volume of one conical hole, (iii) volume of the remaining solid.

 

Answer 1

Height = 10 cm.

Radius

${\displaystyle =\frac{8}{2}}$

${\displaystyle =4cm.}$

(i) Volume of cylinder

${\displaystyle =\pi r^{2}h}$

${\displaystyle =\pi \times {\left(4\right)}^2\times 10}$
= $$160\pi {cm}^3$$

(ii) Volume of conical hole diameter of

cone = 6 cm.

radius ${\displaystyle =\frac{6}{2}}$

           ${\displaystyle =3cm.}$

height = 4 cm.

volume ${\displaystyle =\frac{1}{3}\pi \left(7\right)h}$

              ${\displaystyle =\frac{1}{3}\pi .9.4}$

              ${\displaystyle =12\pi c{m}^3}$

(iii) Volume of remaining solid

${\displaystyle =160\pi -2\times \left(12\pi \right)}$

${\displaystyle =160\pi -24\pi }$

 = $$136\pi {cm}^3$$