Which whole number cube results in a volume closest to 500? A) 7 B) 8 C) 9 D) 6

Understand the Problem

The question is asking which whole number cube, when the side length is used to calculate volume (side length cubed), will yield a volume that is closest to 500. To find the answer, we will calculate the volumes of each cube (6³, 7³, 8³, and 9³) and compare them to 500.

Answer

8, yielding a volume of $512$.

Steps to Solve

Calculate the volume of the cube with side length 6

To find the volume of a cube, we use the formula: $$ V = s^3 $$ where $s$ is the side length.

For a cube with side length 6: $$ V = 6^3 = 6 \times 6 \times 6 = 216 $$

Calculate the volume of the cube with side length 7

Using the same formula: $$ V = 7^3 = 7 \times 7 \times 7 = 343 $$

Calculate the volume of the cube with side length 8

Again, using the formula: $$ V = 8^3 = 8 \times 8 \times 8 = 512 $$

Calculate the volume of the cube with side length 9

Using the formula once more: $$ V = 9^3 = 9 \times 9 \times 9 = 729 $$

Compare the calculated volumes to 500

Now we compare the volumes we calculated:

Volume for side length 6: 216
Volume for side length 7: 343
Volume for side length 8: 512
Volume for side length 9: 729

The closest volume to 500 is 512 from the cube with side length 8.

The whole number cube with a side length closest to a volume of 500 is 8, yielding a volume of $512$.

More Information

The volume of a cube increases rapidly with the increase in side length, as it is calculated by cubing the side length. Understanding this relationship can help us estimate where a specific volume might fall among integers.

Tips

Forgetting to cube the side length correctly. Always ensure to perform the multiplication three times accurately.
Comparing volumes incorrectly; make sure to evaluate which calculated volume is closest to 500.

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