Question

a solid is in the shape of cone standing on a hemisphere with both their radii equal to 1 centimetre and height of the cone is equals to its radius find the volume of the solid in terms of Pi​

Answer 1

Given :

• A solid is the combination of a cone and a hemisphere.
• Radius of base of cone → 1 cm
• Radius of hemispherical part → 1 cm
• Height of cone → 1 cm

So,

Formula Needed

Volume of cone :

$\boxed{\bf{\dfrac{1}{3} \pi r^{2} \times h}}$

Volume of Hemisphere :

$\boxed{\bf{\dfrac{2}{3} \pi r^{3}}}$

For further calculation refer to the attachment.

Answer :

The Volume of solid is π cm³

Answer 2

Given :

• A solid is the combination of a cone and a hemisphere.

• Radius of base of cone, r = 1 cm

• Radius of hemispherical part, r = 1 cm

• Height of cone, h = 1 cm

To find :-

• Volume of solid

Formula Used :-

${{ \boxed{\large{\bold\green{Volume_{(cone)}\: = \:\dfrac{1}{3} \pi r^2h}}}}}$

${{ \boxed{\large{\bold\green{Volume_{(hemi - sphere)}\: = \:\dfrac{2}{3} \pi r^3}}}}}$

Solution :-

$\tt \: Volume_{(solid)} = Volume_{(cone)} + Volume_{(hemi - sphere)}$

$\tt \: \implies \: Volume_{(solid)} = \dfrac{1}{3} \pi \: {r}^{2}h + \dfrac{2}{3} \pi \: {r}^{3}$

$\tt \: \implies \: Volume_{(solid)} = \dfrac{1}{3} \pi \: \times {1}^{2} \times 1+ \dfrac{2}{3} \times \pi \: {(1)}^{3}$

$\tt \: \implies \: Volume_{(solid)} = \dfrac{1}{3}\pi + \dfrac{2}{3} \pi$

$\tt \: \implies \: Volume_{(solid)} \: = \pi \: {cm}^{3}$