Multiple choice

The radius of a sphere is increased by 10%. Its volume increases by

  1. 10%

  2. 12.1%

  3. 13.3%

  4. 33.1%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Volume of a sphere V = (4/3) * pi * r^3. If r increases by 10%, new radius r' = 1.1r. New volume V' = (4/3) * pi * (1.1r)^3 = (4/3) * pi * r^3 * 1.331. The increase is 1.331 - 1 = 0.331, or 33.1%.

AI explanation

The volume of a sphere is calculated using the formula four thirds pi r cubed. If the radius increases by 10 percent, the new radius becomes 1.1 r, making the new volume four thirds pi (1.1 r) cubed, which is 1.331 times four thirds pi r cubed. The increase in volume is 1.331 minus 1, or 0.331, which equals a 33.1 percent increase.

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