Question

Sarah has a pond in the shape of a half sphere in her back yard. The pond currently holds 1,071.79 cubic inches of water. What is the radius of the pond? Sarah wants to double the volume of the pond. What will the new radius be?

Answer 1

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Answer:

• 8 in
• 8∛2 ≈ 10.08 in

Step-by-step explanation:

The volume of a hemisphere is given by the formula ...

  V = (2/3)πr³

Then the radius is ...

  r = ∛(3V/(2π))

  r = ∛(3·1071.79/(2·3.14)) ≈ ∛512.00 ≈ 8.00

The radius of Sarah's pond is 8 inches.

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We can see from the above that the radius is proportional to the cube root of the volume. If Sarah wants to double the volume, she needs to multiply the radius by ∛2 ≈ 1.260.

The new radius will be 8∛2 ≈ 10.08 inches.