Question

Volume of composite figures

Answer 1

Given:

The diameter of cylinder is 6 in and the height of the cylinder is 8 in.

The dimensions of the cuboid are 15 in by 9 in by 9 in.

To find:

The volume of the composite figure.

Solution:

Volume of a cuboid is:

$V_1=length\times breadth\times height$

$V_1=15\times 9\times 9$

$V_1=1215$

So, the volume of the cuboid is 1215 cubic inches.

The diameter of cylinder is 6 in. So, the radius of the cylinder is:

$\dfrac{6}{2}=3\text{ inches}$

Volume of a cylinder is:

$V_2=\pi r^2h$

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

Substituting $r=3,h=8,\pi =3.14$, we get

$V_2=(3.14)(3)^2(8)$

$V_2=(3.14)(9)(8)$

$V_2=226.08$

The volume of the cylinder is 226.08 cubic inches.

Now, the volume of the composite figure is:

$V=V_1+V_2$

$V=1215+226.08$

$V=1441.08$

Therefore, the volume of the composite figure is 1441.08 cubic inches.