Question

a cone of radius 4cm is divided into 2 parts by drawing a plane through midpoint of its axis parallel to it's base . compare the volumes of two parts. show the answer step by step

Answer 1

this is the answer for your question

Answer 2

Answer:

volume of bottom part is 7 times the volume of top part.

Step-by-step explanation:

A cone of radius 4 cm is divided into 2 parts by drawing a plane through mid point of its axis parallel to it's base.

Please see the attachment for figure.

We got two parts Top and bottom

Top part is shape of cone whose height is h and radius r

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

Volume of Top part $=\frac{1}{3}\times \pi\times r^2\times h$

Bottom part is shape of frustum whose height is h and top radius r and bottom radius R.

Using similar theorem property, ΔOAD ≈ΔOBC

$\therefore \dfrac{OA}{OB}=\dfrac{AD}{BC}$

$\dfrac{h}{2h}=\dfrac{r}{R}$

R=2r

Volume of bottom part $=\frac{1}{3}\times \pi\times h(R^2+r^2+Rr)$

Volume of bottom part $=\frac{1}{3}\times \pi\times h(4r^2+r^2+2r^2)=\frac{1}{3}\times \pi\times h\times 7r^2$

Now we find the ratio of both volume $\dfrac{\frac{1}{3}\times \pi\times r^2\times h}{\frac{1}{3}\times \pi\times h\times 7r^2}$

Ratio = 1:7

Hence, volume of bottom part is 7 times the volume of top part.