Question

6. Joe is making a pyramid for school. He thinks he wants to use sugar cubes. He found a box in the back of his pantry, but the label was torn that tells the number of cubes. He needs 91 cubes. He measures the box, and it is 3 x 312 x 1 12inches. He knows a sugar cube measures 12 inches on a side. Will he have enough sugar cubes to make a pyramid? What is the volume of the cubes in the box?

Answer 1

Joe will not have enough sugar cubes; his box only contains 63 cubes and he needs 91 to make the pyramid. The box's volume is 15.75 cubic inches and each sugar cube has a volume of ¼ cubic inch.

Step-by-step explanation:

To determine if Joe has enough sugar cubes to make a pyramid requiring 91 cubes, we need to calculate the volume of the sugar cubes in the box he found. The box measures 3 x 3½ x 1½ inches.

Since a sugar cube measures ½ inch on a side, its volume is ½³, which equals ¼ cubic inch per cube.

First, we calculate the volume of the box:

• Volume of the box = length x width x height
• Volume of the box = 3 in. x 3½ in. x 1½ in.
• Volume of the box = 15.75 cubic inches

Next, we determine how many sugar cubes the box can hold:

Number of cubes in the box = Volume of the box / Volume of one sugar cubeNumber of cubes in the box = 15.75 cubic inches / ¼ cubic inch per cubeNumber of cubes in the box = 63

Since Joe requires 91 sugar cubes and the box only contains 63 cubes, he will not have enough sugar cubes from this box to make the pyramid.