Question

A vendor is using an 8ft by 8ft tent for a craft fair. The legs of the tent are 9ft y’all and the top forms a square pyramid with a height of 3ft. What is the volume, in cubic feet, of space the tent occupies

Answer 1

640 ft^3

Explanation:

In this case we must divide the area into two parts, in the prism and in the pyramid, the sum of the volume of these parts would be the total volume

However

for the volume of the prism it would be the multiplication of the three sides, that is:

8 * 8 * 9 = 576

i.e. 576 ft ^ 3

For the pyramid, the formula is the multiplication of the area of the base by the height divided by 3, we know that the area of the base is 8 * 8 and that the height is 3, therefore:

8 * 8 * 3/3 = 64

64 ft ^ 3 is the volume of the pyramid

The total would be:

576 + 64 = 640

Total volume would be 640 ft ^ 3