120k views
5 votes
5. A rectangular pyramid fits exactly on top of a rectangular prism. The prism has *

a length of 12 cm, a width of 6 cm, and a height of 8 cm. The pyramid has a
height of 18 cm. Find the volume of the composite space figure
O 1728 cm^3
576 cm^3
1008 cm^3
432 cm^3
Back
Next
Page 4 of 9
Clear form

User Jonas T
by
9.1k points

1 Answer

6 votes

Explanation:

The volume of a rectangular prism is given by:

V_prism = length x width x height

Substituting the given values, we get:

V_prism = 12 cm x 6 cm x 8 cm

V_prism = 576 cm^3

The volume of a rectangular pyramid is given by:

V_pyramid = (1/3) x base area x height

The base of the pyramid is a rectangle with length and width equal to the base of the prism, which is 12 cm and 6 cm. Therefore, the base area is:

base area = length x width = 12 cm x 6 cm = 72 cm^2

Substituting the given and calculated values, we get:

V_pyramid = (1/3) x 72 cm^2 x 18 cm

V_pyramid = 432 cm^3

The total volume of the composite space figure is the sum of the volumes of the prism and the pyramid:

V_total = V_prism + V_pyramid

V_total = 576 cm^3 + 432 cm^3

V_total = 1008 cm^3

Therefore, the volume of the composite space figure is 1008 cm^3. The answer is C. 1008 cm^3.

User GrvTyagi
by
8.0k points

No related questions found