Find the volume of a pyramid with a square base, where the perimeter of the base is 10.4\text{ in}10.4 in and the height of the pyramid is 9.6\text{ in}9.6 in. Round your answer to the nearest tenth of a cubic inch.

21.6in^3

Step-by-step explanation:

\text{Volume of Pyramid:}

Volume of Pyramid:

V=\frac{1}{3}Bh

V=  

3

1

​  

Bh

Where B is the area of the base

\text{Perimeter of base}:

Perimeter of base:

\,\,10.4

10.4

\text{Side length of base}:

Side length of base:

\,\,\frac{10.4}{4}=2.6

4

10.4

​  

=2.6

Divide perimeter of square by 4 to get side length

\text{Area of base}:

Area of base:

\,\,2.6^2=6.76

2.6  

2

=6.76

Area of a square is s^2

B=

B=

\,\,6.76

6.76

h=

h=

\,\,9.6

9.6

given

V=

V=

\,\,\frac{1}{3}Bh

3

1

​  

Bh

V=

V=

\,\,\frac{1}{3}(6.76)(9.6)

3

1

​  

(6.76)(9.6)

Plug in

V=

V=

\,\,21.632

21.632

V\approx

V≈

\,\,21.6\text{ in}^3

21.6 in  

3