Question

Find the volume of each figure

Answer 1

Answer:

See explanation

Step-by-step explanation:

1. The first figure shows triangular prism. The volume of the triangular prism is

$V=\text{Base area}\times \text{Height}$

The base of this triangular prism is the triangle with the base of 7 cm and height of $h$ cm (it is not seen).

The base area is

$\text{Base area}=\dfrac{1}{2}\times \text{Base}\times \text{Height}=\dfrac{1}{2}\times 7\times h=\dfrac{7h}{2}\ cm^2$

and the volume of the prism is

$V=\dfrac{7h}{2}\times 13=\dfrac{91h}{2}\ cm^3$

Just substitute the length of the height and calculate the volume.

2. The second figure shows square pyramid. The volume of the square pyramid is

$V=\dfrac{1}{3}\times \text{Base area}\times \text{Height}$

The base of this square pyramid is the square with the side length of 4 yd.

The base area is

$\text{Base area}= \text{Side Lenght}^2=4^2 =16\ yd^2$

and the volume of the pyramid is

$V=\dfrac{1}{3}\times 16\times 12=64\ yd^3$