In the volume formula for a sphere, which exponent is used on the radius?

In the volume formula for a sphere, which exponent is used on the radius?

• A. 3
• B. 2
• C. 4
• D. 1

Answer: (A)

Volume is a three-dimensional measure, so it grows with the radius in three directions. That’s why the radius appears with an exponent of 3 in the sphere’s volume formula: V = (4/3)π r^3. If you scale the radius by a factor k, the volume scales by k^3. For example, doubling the radius makes the volume eight times bigger. That cubic relationship rules out the other exponents: squaring would imply the volume grows like area, not volume; multiplying by the radius alone would only double the product; a higher exponent would make volume grow even faster than observed. So the exponent on the radius is 3.

Volume is a three-dimensional measure, so it grows with the radius in three directions. That’s why the radius appears with an exponent of 3 in the sphere’s volume formula: V = (4/3)π r^3.

If you scale the radius by a factor k, the volume scales by k^3. For example, doubling the radius makes the volume eight times bigger. That cubic relationship rules out the other exponents: squaring would imply the volume grows like area, not volume; multiplying by the radius alone would only double the product; a higher exponent would make volume grow even faster than observed.

So the exponent on the radius is 3.