Math problem help!

Question

The largest pyramid in the world is in Cholula, Mexico. Its base area is 1,960,000(feet squared) and its height is 177ft

a) what id its volume?

b) about how many hotel rooms, each 30 ft by 25 ft by 10 ft, would it take to make the same volume?

show work to help thanks!!

Answer 1

1) The equation of the volume of a pyramid can be written as V = (1/3)A_bh, where A_b is the area of the base and h is the height. You are given the area of the base as 1,960,000 ft² and the height as 177 ft. To find the volume, plug in the values and solve.

V = (1/3)A_bh

V = (1/3)(1,960,000 ft²)(177 ft)

V = 115,640,000 ft³

2) The volume of a rectangular prism (which would be the shape of a hotel room) is V = lwh = (length)(width)(height). First find the volume of one hotel room.

V = lwh

V = (30 ft)(25 ft)(10 ft)

V = 7500 ft³

To find how many hotel rooms would make up the same volume, divide the pyramid volume by the rectangular prism volume.

# of hotel rooms = V_pyramid / V_{hotel room}

# of hotel rooms = 115,640,000 ft³ = 15418.667

7500 ft³

About 15,419 hotel rooms would make the same volume.