Question

Find the volume of a pyramid with a square base, where the perimeter of the base is 8.2\text{ cm}8.2 cm and the height of the pyramid is 13\text{ cm}13 cm. Round your answer to the nearest tenth of a cubic centimeter.

Answer 1

Answer:

$V=18.2cm^3$

Step-by-step explanation:

The volume of the pyramid is given by:

$V=\frac{A_{b}h}{3}$

where $A_{b}$ is the area of the base and $h$ is the height.

We know that the height is:

$h=13cm$

Thus we need to find the area of the square at the base.

The perimeter of the square is:

$p=8.2cm$

this means that the length of the sides of the square is :

$l=\frac{p}{4}\\ \\l=\frac{8.2cm}{4}\\ \\l=2.05cm$

Now we can find the area of the base which the area of the square:

$A_{b}=l^2\\A_b=(2.05cm)^2\\A_b=4.2025cm^2$

and finally we find the volume:

$V=\frac{A_{b}h}{3}$

$V=\frac{(4.2025cm^2)(13cm)}{3}\\ \\V=\frac{54.6325cm^3}{3}\\ \\V=18.2108cm^3$

Which rounded to the nearest tenth of a cubic centimeter is: $V=18.2cm^3$