Question 1: Calculate the surface area of a sphere with radius 5 cm. Use 4πr² for your calculation.

Answer: 314.16

Question 2: Find the surface area of a sphere with radius 3.5 meters. Show your working.

Answer: 153.94

Question 3: A sphere has a radius of 2 cm. What is its surface area? (Use 3.14 for π.)

Answer: 50.24

Question 4: Calculate the surface area of a sphere with radius 6 inches. Use 3.14 for π.

Answer: 452.16

Question 1: A spherical globe has a radius of 10 cm. If a new globe has a radius double that of the original, what is the difference in their surface areas? Show your calculations.

Answer: 1256.64

Question 2: Explain why doubling the radius of a sphere results in quadrupling its surface area.

Answer: Because surface area is proportional to r², doubling r results in 2²=4 times the surface area.

Question 3: A spherical ball has a surface area of 628.32 cm². Find its radius.

Answer: 10

Question 4: If the radius of a sphere is decreased by 25%, what happens to its surface area? Explain your reasoning.

Answer: Surface area decreases to approximately 56.25% of the original, since it is proportional to r².

Question 1: A sports company is producing spherical basketballs with a radius of 12 cm. Calculate the total surface area that needs to be painted on one ball.

Answer: 1809.6

Question 2: A glass sphere has a radius of 8 inches. If a coating of paint costs $0.05 per square centimeter, how much will it cost to paint the entire surface?

Answer: Cost depends on converting inches to centimeters; approximate surface area is 1612.96 cm², so cost ≈ $80.65

Question 1: A sphere's surface area is increased by 50%. What is the new radius if the original radius was 4 cm? Show your calculations.

Answer: 6.4

Question 2: Design a problem involving two spheres where the surface areas are in a ratio of 1:4. If the smaller sphere has a radius of 3 cm, find the radius of the larger sphere.

Answer: The larger sphere’s radius is 6 cm.

Question 1: Calculate the surface area of a sphere with radius 7 cm, using 3.14 for π.

Answer: 615.44

Question 2: A spherical container has a radius of 15 inches. Find the surface area and determine if it can be painted with a single coat of paint costing $0.10 per square inch.

Answer: Surface area = 4*3.14*15²=2827.5 in²; cost = $282.75; Yes, it can be painted with one coat.

Question 1: A student calculates the surface area of a sphere with radius 4 cm as 50 cm², using 4πr² and π=3.14. Identify the mistake and provide the correct answer.

Answer: Incorrectly approximated 4πr²; correct surface area = 201.06 cm²

Question 2: A student forgets to square the radius when calculating surface area, using 4πr instead of 4πr². Explain why this mistake leads to an incorrect answer.

Answer: Because surface area depends on r squared, not r, omitting the square results in a wrong, smaller value.