Question

Find the volume of the figure: an oblique cylinder next to a cube.

Answer 1

Answer:

$(2,200\pi +8,000)\ ft^{3}$

Step-by-step explanation:

we know that

The volume of the figure is equal to the volume of cube plus the volume of the cylinder

step 1

Find the volume of the cube

The volume of the cube is equal to

$V=b^{3}$

we have

$b=2(10)=20\ ft$ ----> the length side of the cube is equal to the diameter of the cylinder

so

$V=20^{3}=8,000\ ft^{3}$

step 2

Find the volume of the cylinder

The volume of the cylinder is equal to

$V=\pi r^{2} h$

we have

$r=10\ ft$

$h=42-20=22\ ft$

substitute

$V=\pi (10)^{2} (22)$

$V=2,200\pi\ ft^{3}$

step 3

The volume of the figure is equal to

$(2,200\pi +8,000)\ ft^{3}$