If the diameter of a sphere is 10 cm, what is its volume? (2023)

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Question: If the diameter of a sphere is 10 cm, what is its volume? (2023)

Options:

Correct Answer: 200π cm³

Exam Year: 2023

Solution:

The volume of a sphere is given by V = (4/3)πr³. The radius r = diameter/2 = 5 cm. Thus, V = (4/3)π(5)³ = (4/3)π(125) = 500/3 π cm³.

If the diameter of a sphere is 10 cm, what is its volume? (2023)

If the diameter of a sphere is 10 cm, what is its volume? (2023)

Step 1: Identify the diameter of the sphere, which is given as 10 cm.
Step 2: Calculate the radius of the sphere by dividing the diameter by 2. So, radius r = 10 cm / 2 = 5 cm.
Step 3: Use the formula for the volume of a sphere, which is V = (4/3)πr³.
Step 4: Substitute the radius into the formula. So, V = (4/3)π(5)³.
Step 5: Calculate (5)³, which is 5 * 5 * 5 = 125.
Step 6: Now substitute this value back into the volume formula: V = (4/3)π(125).
Step 7: Multiply (4/3) by 125 to get (500/3). So, V = (500/3)π cm³.
Step 8: The final answer for the volume of the sphere is (500/3)π cm³.

Volume of a Sphere – Understanding the formula for the volume of a sphere and how to apply it using the radius derived from the diameter.
Unit Conversion – Ensuring that all measurements are in the same units, though in this case, it is straightforward as all dimensions are in centimeters.