Question

A builder decides to construct a new building in the shape of a regular square pyramid with base sides of 100 feet and a vertical height of 120 feet. If each office in the building will take up 1,500 cubic feet of space, approximately how many offices will fit in the building?

Answer 1

266 offices will fit in the square pyramid-shaped building.

Explanation:

To find out how many offices will fit in the square pyramid-shaped building, we need to calculate the volume of the building and then divide it by the volume of each office.

The volume of a square pyramid is given by the formula:

V = (1/3) * base area * height

In this case, the base sides of the pyramid are 100 feet, so the base area is 100^2 = 10,000 square feet. The height of the pyramid is 120 feet.

Substituting these values into the formula, we can calculate the volume of the building:

V = (1/3) * 10,000 * 120 = 400,000 cubic feet

Now, we can divide the volume of the building by the volume of each office (1,500 cubic feet) to find out approximately how many offices will fit:

Number of offices = 400,000 / 1,500

≈ 266.67

Since we cannot have a fraction of an office, we round down to the nearest whole number.

Therefore,

266 offices will fit in the square pyramid-shaped building.