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If a sphere has a volume of 288π cubic centimeters, what is its radius?

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Question: If a sphere has a volume of 288π cubic centimeters, what is its radius?

Options:

  1. 6 cm
  2. 8 cm
  3. 9 cm
  4. 10 cm

Correct Answer: 8 cm

Solution: 

The volume of a sphere is given by V = (4/3)πr³. Setting (4/3)πr³ = 288π, we find r³ = 216, thus r = 6 cm.

If a sphere has a volume of 288π cubic centimeters, what is its radius?

Practice Questions

Q1
If a sphere has a volume of 288π cubic centimeters, what is its radius?
  1. 6 cm
  2. 8 cm
  3. 9 cm
  4. 10 cm

Questions & Step-by-Step Solutions

If a sphere has a volume of 288π cubic centimeters, what is its radius?
  • Step 1: Write down the formula for the volume of a sphere, which is V = (4/3)πr³.
  • Step 2: Substitute the given volume (288π) into the formula: (4/3)πr³ = 288π.
  • Step 3: To simplify, divide both sides of the equation by π: (4/3)r³ = 288.
  • Step 4: Multiply both sides by 3 to eliminate the fraction: 4r³ = 864.
  • Step 5: Now, divide both sides by 4: r³ = 216.
  • Step 6: To find the radius (r), take the cube root of 216: r = 6 cm.
  • Volume of a Sphere – Understanding the formula for the volume of a sphere, V = (4/3)πr³, and how to manipulate it to find the radius.
  • Algebraic Manipulation – Ability to isolate variables and solve for r in the equation derived from the volume formula.
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