Question

A cube-shaped box has a side length of 4n³ centimeters. Anesha has several cube-shaped blocks with a side length of 3n centimeters that she needs to store in the box. How many blocks can she store in the box?

a) 64n³
b) 48n³
c) 36n⁴
d) 12n⁴

Answer 1

To find the number of cube-shaped blocks that can be stored in the cube-shaped box, calculate the volumes of the box and the blocks and then divide the volume of the box by the volume of each block.

Step-by-step explanation:

To find the number of cube-shaped blocks that can be stored in the cube-shaped box, we need to determine the volume of the box and the volume of each block. The volume of the cube-shaped box is given by the formula V = s³, where s is the side length of the box. In this case, s = 4n³. Therefore, the volume of the box is (4n³)³ = 64n⁹.

The volume of each cube-shaped block is given by the formula V = s³, where s is the side length of the block. In this case, s = 3n. Therefore, the volume of each block is (3n)³ = 27n³.

To determine the number of blocks that can be stored in the box, we divide the volume of the box by the volume of each block: (64n⁹) / (27n³) = 64n⁹ / 27n³ = 64/27 = 2⅓.

Therefore, Anesha can store approximately 2⅓ cube-shaped blocks in the box.