Question

Curtis build a dog house with base shaped like a cube and a roof shaped like a pyramid. The cube has an edge lenght of 3 1/2 feet. The height of the pyramid is 5 feet. Find the volume of the doghouse rounded to the nearest tenth.

Answer 1

The volume of the cube is:
V1 = L ^ 3
Where,
L: length of the sides of the cube.
Substituting we have:
V1 = (3 + 1/2) ^ 3
V1 = 42,875 feet ^ 3
The volume of the pyramid is:
V2 = ((Ab) * (h)) / (3)
Where,
Ab: base area
h: height
Substituting we have:
V2 = (((3 1/2) * (3 1/2)) * (5)) / (3)
V2 = 20.41666667 feet ^ 3
The volume of the house is the sum of both volumes:
V1 + V2 = 42,875 feet ^ 3 + 20.41666667 feet ^ 3
V1 + V2 = 63.29166667 feet ^ 3
Nearest tenth:
V1 + V2 = 63.3 feet ^ 3
Answer:
The volume of the doghouse rounded to the nearest tenth is:
V1 + V2 = 63.3 feet ^ 3