Question 1: Calculate the volume of a sphere with a radius of 5 cm using the formula ⁴⁄₃πr³.

Answer: 523.6

Question 2: Find the radius of a sphere if its volume is 1000 cm³. (Use π ≈ 3.14)

Answer: ≈5.42

Question 3: A sphere has a radius of 3 cm. What is its volume? (Use π ≈ 3.14)

Answer: 113.1

Question 1: A spherical globe has a radius of 10 cm. Calculate its volume. Then, determine how much material is needed if the globe is made of a material costing $0.05 per cm³.

Answer: Approximately 4188.8 cm³; Cost ≈ $209.44

Question 2: Explain why using an approximation of π affects the accuracy of your volume calculation for a sphere.

Answer: Using an approximation of π introduces a small error into the volume calculation, making the result slightly less accurate than using the exact value of π.

Question 1: A sports ball is a perfect sphere with a radius of 12 cm. Calculate the volume of the ball and suggest how much space it occupies in a container.

Answer: 7238.2 cm³

Question 2: A water tank is spherical with a diameter of 4 meters. How much water (in cubic meters) can it hold?

Answer: 33.51

Question 1: A sphere's volume is doubled when its radius is increased from 4 cm to a new radius r. Find r.

Answer: ≈6.35 cm

Question 2: Derive the formula for the volume of a sphere starting from the formula for the volume of a cylinder and explaining the relationship.

Answer: [Expected discussion on the limits of integration or geometric reasoning leading to ⁴⁄₃πr³]

Question 1: A student calculates the volume of a sphere with radius 7 cm as 700 cm³. Identify and correct the mistake.

Answer: Incorrect; actual volume ≈ 1436.8 cm³, using ⁴⁄₃πr³

Question 2: Calculate the volume of a sphere with radius 8 cm using π ≈ 3.14. Show your working and compare with the exact value if π = 3.14159.

Answer: ≈2144.66 cm³ (approximate), exact ≈2144.66 cm³