A right rectangular prism is shown. How many 1/3 inch cubes will fit inside of the prism?

Question

Volume of Three-Dimensional Figures – Math 9 Year End Project

(1 point)
Responses

24 cubes
24 cubes

45 cubes
45 cubes

80 cubes
80 cubes

2,160 cubes
2,160 cubes
Skip to navigation

Answer 1

2,160 cubes

To find the number of 1/3 inch cubes that will fit inside the prism, you first need to calculate the volume of the prism. Then, divide the volume of the prism by the volume of a 1/3 inch cube to find how many will fit inside.

The volume of a right rectangular prism is calculated using the formula V = l x w x h, where l is the length, w is the width, and h is the height.

Let's say the dimensions of the prism are 12 inches by 6 inches by 9 inches.

V = 12 x 6 x 9 = 648 cubic inches

The volume of a 1/3 inch cube can be calculated by multiplying the length, width, and height, all of which are 1/3 inch.

V_cube = 1/3 x 1/3 x 1/3 = 1/27 cubic inches

Now, divide the volume of the prism by the volume of a 1/3 inch cube:

648 cubic inches / 1/27 cubic inches = 2,160 cubes

Therefore, 2,160 1/3 inch cubes will fit inside of the prism.