Question

Curtis builds a doghouse with base shaped like a cube and a roof shaped like a pyramid. the cube has an edge length 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 dog house will be given by:
Total volume=(volume of the cube)+(volume of the pyramid)
volume of the cube is given by:
V1=(length)*(width)*(height)
from the info:
(length)=(width)=(height)=3 1/2 ft
hence;
V1=(3 1/2)×(3 1/2)×(3 1/2)=42 7/8=42.875 ft³

volume of the pyramid is given by:
v2=(lwh)/3
V2=1/3(base area)×(height)
V2=1/3(3.5×3.5)×(5)
V2=245/12=20 5/12 ft³
Hence the total volume of the whole house will be:
(42 7/8+20 5/12)
=63 7/24 ft³