Question

A cone of radius 10cm is cut into two parts by a plane through the mid point of its vertices axis parallel to the base .Find the ratio of the volume of the smaller cone and frustum of the cone​

Answer 1

$\red{\textbf{Answer :- 1:7}}$

Step-by-step explanation:

$radius \: of \: cone \: = 10cm$

$Volume \: of \: cone= \:$

$\LARGE\frac{1}{3} \small\pi {r}^{2} _{1} \: h_{1}$

$= \LARGE \frac{1}{3} \pi( \frac{r}{2} {)} ^{2} \small \times \LARGE \frac{h}{2}$

$= \LARGE \frac{1}{3} \pi( \frac{10}{2} {)}^{2} \small \times \LARGE \frac{h}{2}$

$=\LARGE \frac{25\pi \: h}{6} \small \: {cm}^{3}$

$Volume \: of \: frustum \: ABCD=$

$\LARGE \frac{1}{3} \small \pi h_{2}( {R}^{2} + {r}^{2} + Rr)$

$=\LARGE \frac{1}{3} \pi \small\times \LARGE \frac{h}{2} \small( {10}^{2} + {5}^{2} + 10 \times 5)$

$= \LARGE \frac{175\pi \: h}{6}$

$Required \: ratio ,$

$= \: \LARGE\frac{ \frac{25\pi \: h}{6} }{ \frac{175\pi \: h}{6} } = \frac{25}{175}$

$= \LARGE \frac{1}{7}$

$\red{\textbf{ = 1:7}}$