Question

Need to find volume, step by step explanation pls



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Answer 1

Given:

A figure of combination of hemisphere, cylinder and cone.

Radius of hemisphere, cylinder and cone = 6 units.

Height of cylinder = 12 units

Slant height of cone = 10 units.

To find:

The volume of the given figure.

Solution:

Volume of hemisphere is:

`V_1=(2)/(3)\pi r^3`

Where, r is the radius of the hemisphere.

`V_1=(2)/(3)(3.14)(6)^3`

`V_1=(6.28)/(3)(216)`

`V_1=452.16`

Volume of cylinder is:

`V_2=\pi r^2h`

Where, r is the radius of the cylinder and h is the height of the cylinder.

`V_2=(3.14)(6)^2(12)`

`V_2=(3.14)(36)(12)`

`V_2=1356.48`

We know that,

`l^2=r^2+h^2` [Pythagoras theorem]

Where, l is length, r is the radius and h is the height of the cone.

`(10)^2=(6)^2+h^2`

`100-36=h^2`

`√(64)=h`

`8=h`

Volume of cone is:

`V_3=(1)/(3)\pi r^2h`

Where, r is the radius of the cone and h is the height of the cone.

`V_3=(1)/(3)(3.14)(6)^2(8)`

`V_3=(25.12)/(3)(36)`

`V_3=301.44`

Now, the volume of the combined figure is:

`V=V_1+V_2+V_3`

`V=452.16+1356.48+301.44`

`V=2110.08`

Therefore, the volume of the given figure is 2110.08 cubic units.