Question

What is the total volume of the composite figure?

The composite figure is made up of two congruent
rectangular pyramids joined at their bases.

a. 30 cubic units

b. 60 cubic units

c. 120 cubic units

d. 180 cubic units

Answer 1

B. 60 cubic units

Explanation:

The formula for the volume of a pyramid:

`V=(1)/(3)Bh`

B is the base area. Find this first:

We are given the length and width of the rectangle, so find the area:

`B=7.5*2\\B=15`

The base area shared by the pyramids is 15. Insert this into the formula:

`V=(1)/(3)(15)h`

Find the height:

We are told that one height for the pyramid is 6, and the total height of both is 12. This means that both have the same height of 6. Insert this into the formula:

`V=(1)/(3)(15)(6)`

Solve:

`V=(1*15*6)/(3)\\\\ V=(90)/(3) \\\\V=30`

The volume of one pyramid is 30. Multiply this by 2 since there are two pyramids:

`V=30*2\\V=60`

The total volume of the figure is 60 units³.