Multiple choice

What will be the left over amount of wood when a hemisphere with radius 10.5 cm is chiseled out of a wooden cube of edge 21 cm?

  1. 8957.82 cm3

  2. 6863 cm3

  3. 6835.5 cm3

  4. 1984.5 cm3

  5. 210 cm2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The cube's volume is 21^3 = 9261 cm^3. The hemisphere volume is (2/3) x (22/7) x 10.5^3 = 2425.5 cm^3, so the leftover volume is 9261 - 2425.5 = 6835.5 cm^3.

AI explanation

The volume of the wooden cube is 21 cubed, which equals 9261 cubic cm. The formula for the volume of a hemisphere is two thirds times pi times radius cubed, so substituting the radius of 10.5 gives 2425.5 cubic cm. Subtracting the hemisphere's volume from the cube's volume gives 9261 minus 2425.5, leaving 6835.5 cubic cm of wood. The correct answer is 6835.5 cm^3.

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