A sphere has a diameter of 10 cm. What is its surface area?

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Question: A sphere has a diameter of 10 cm. What is its surface area?

Options:

Correct Answer: 314.16 cm²

Solution:

Surface Area = 4πr² = 4π(5)² = 100π ≈ 314.16 cm²

A sphere has a diameter of 10 cm. What is its surface area?

A sphere has a diameter of 10 cm. What is its surface area?

Step 1: Understand that the diameter of the sphere is given as 10 cm.
Step 2: Find the radius of the sphere. The radius is half of the diameter, so divide 10 cm by 2. This gives you a radius of 5 cm.
Step 3: Use the formula for the surface area of a sphere, which is Surface Area = 4πr².
Step 4: Substitute the radius (5 cm) into the formula. This means you calculate 4π(5)².
Step 5: Calculate (5)², which is 25.
Step 6: Now multiply 4 by π and then by 25. This gives you 100π.
Step 7: If you want a numerical approximation, calculate 100π, which is approximately 314.16 cm².

Surface Area of a Sphere – The formula for the surface area of a sphere is derived from its radius, which is half of the diameter.
Understanding Diameter and Radius – The diameter is twice the radius, and it's crucial to convert diameter to radius when using the surface area formula.