Question

From a solid cylinder with height 14cm
and radius of the base 6com, a Conical
cavity fl the same height and some
diameter is hollowed out. Find the
volume of the
the remaing solid.​

Answer 1

$\underline {\pink{ Dimensions \:of \: a \:solid \: cylinder : }}$

$Height (h) = 14 \:cm$

$Redius \: of \: the \: cylinder (r) = 6 \:cm$

/* According to the problem given */

a Conical cavity of the same height and some

the same height and somediameter is hollowed out from the solid.

$Volume \: of \: the \: remaining \:solid$

$= Volume \: of \: the \: solid \:cylinder -$

$Volume \:of \: conical \:cavity$

$= \pi r^{2} h - \frac{1}{3} \times \pi r^{2} h$

$= \Big( 1 - \frac{1}{3}\Big)\pi r^{2} h$

$= \Big( \frac{3-1}{3}\Big)\pi r^{2} h$

$= \frac{2}{3}\times \pi r^{2} h$

$= \frac{2}{3} \times \frac{22}{7} \times 6^{2} \times 14$

$= 2 \times 22 \times 6 \times 2 \times 2$

$= 1056 \:cm^{3}$

Therefore.,

$\red{Volume \: of \: the \: remaining \:solid}$

$\green{= 1056 \:cm^{3}}$

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