Question

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

Answer 1

Given,

Height of the cylinder, $H=10cm$

Diameter of Base of the cylinder, $d=8cm$

Hence, the radius of the cylinder, $R=\frac{d}{2}=4cm$

Two conical holes are cutoff from the cylinder.

Height of the cone $h=4cm$

Diameter of the cone $D=6cm$

Hence, Radius of the cone, $r=\frac{D}{2}=3cm$

Now,

Volume of the cylinder $V=\pi R^{2}H$

$V=\pi \times 4^2\times 10c{m}^3$

$V=\pi \times 16\times 10c{m}^3$

$V=160\pi c{m}^3$

Hence, volume of cylinder is $160\pi c{m}^3$

Volume of the cone $v=\frac{1}{3}\pi r^{2}h$

$v=\frac{1}{3}\times \pi \times 3^2\times 4c{m}^3$

$v=\pi \times 3\times 4c{m}^3$

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

Hence, volume of one conical hole is $12\pi c{m}^3$

The volume of the remaining solid = Volume of the cylinder - 2 (Volume of the cone )

$=(160-2\times 12)\pi c{m}^3$

$=(160-24)\pi c{m}^3$

$=136\pi c{m}^3$

Hence, volume of remaining solid is $136\pi c{m}^3$