Question 1: Calculate the surface area of a sphere with a radius of 3 cm.

Answer: 4 * π * 3^2 = 36π ≈ 113.1 cm²

Question 2: If the surface area of a sphere is 125.6 cm², find its radius.

Answer: r = √(125.6 / 4π) ≈ 3.16 cm

Question 3: A sphere has a radius of 5 meters. What is its surface area?

Answer: 4 * π * 5^2 = 100π ≈ 314.2 m²

Question 4: Calculate the surface area of a sphere with radius 7 cm.

Answer: 4 * π * 7^2 = 196π ≈ 615.75 cm²

Question 5: A spherical ball has a surface area of 188.5 cm². What is its radius? (Use π ≈ 3.14)

Answer: r = √(188.5 / 4π) ≈ 3 cm

Question 6: Construct a sphere with a radius of 4 cm on the grid. Then, calculate its surface area.

Answer: 4 * π * 4^2 = 64π ≈ 201.1 cm²

Question 7: A toy globe has a surface area of approximately 502.4 cm². What is the radius of the globe?

Answer: r = √(502.4 / 4π) ≈ 6.3 cm

Question 8: A sphere’s surface area is tripled when its radius increases from 2 cm to a new radius r. Find r.

Answer: Since surface area is proportional to r², 4πr² = 3 * (4π * 2²) => r² = 3 * 4 => r = √12 ≈ 3.46 cm

Question 9: Explain why the surface area of a sphere increases faster than its volume as radius increases.

Answer: Surface area is proportional to r², while volume is proportional to r³. As r increases, r³ grows faster than r², so surface area increases at a slower rate compared to volume.

Question 10: A sphere’s surface area is 150 cm². If the radius increases by 50%, what is the new surface area?

Answer: Original r: r = √(150 / 4π) ≈ 3.1 cm. New radius: r' = 1.5 * 3.1 ≈ 4.65 cm. New surface area: 4 * π * (4.65)^2 ≈ 272.3 cm²

Question 11: Identify and correct the mistake in this calculation: The surface area of a sphere with radius 6 cm is calculated as 4 * π * 6 = 24π.

Answer: Incorrect because the formula is 4πr², so it should be 4 * π * 6^2 = 4 * π * 36 = 144π.