Question

a solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius find the volume of the solid.​

Answer 1

Question :-

A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius find the volume of the solid.

Given :-

Radius of cone = Radius of hemisphere = 1cm

Height of cone = 1cm

To find :-

Volume of solid

Solution :-

Radius of Cone = Radius of hemisphere (R) = 1cm

Height of Cone (H) = 1cm

Formula used :-

$\sf\Large Volume\:of\:cone = \dfrac{1}{3}\pi R^2 H$

$\sf\Large Volume\:of\:hemisphere= \dfrac{2}{3}\pi R^3$

$Volume\:of \:solid \:= \:volume\: of \:cone \:+ volume\: of \:hemisphere$

$\sf = \dfrac{1}{3}\pi R^2 H + \dfrac{2}{3}\pi R^3$

$\sf = \dfrac{1}{3}\pi R^2 (H+2R)$

$\sf = \dfrac{1}{3}\pi \times 1\times 1 (1+2\times 1)$

$\sf = \dfrac{1}{3}\pi \times 3$

$\sf = \dfrac{3\pi }{3}$

$\sf = \pi cm^3$

$\sf\Large Hence,\:volume\:of\:solid\: = \pi cm^3$

Answer 2

Answer:

$\pi {cm}^{3}$

Step-by-step explanation:

☞Radius of cone = Radius of Hemisphere = 1cm

☞Height of cone = 1cm

☞Volume of solid -:

☞Radius of cone = Radius of hemisphere = 1cm

☞Height of Cone = 1cm

$\dfrac{1}{3}\pi R^2 h$

$\dfrac{2}{3}\pi R^3Volumeofhemisphere= </p><p>3$

Volume of solid = volume of cone + volume of hemisphere

Volume of solid = volume of cone + volume of hemisphere

$\dfrac{1}{3}\pi R^2 H + \dfrac{2}{3}\pi R^3$

$\dfrac{1}{3}\pi R^2 (H+2R)$

$\dfrac{1}{3}\pi \times 1\times 1 (1+2\times 1)$

$\dfrac{1}{3}\pi \times 3$

$\dfrac{3\pi }{3}$

$\pi cm^3=πcm$

$volume \: of \: solid \: = \pi cm^3$