Question 1: Calculate the volume of a sphere with a radius of 5 cm.

Answer: 523.6

Question 2: Find the volume of a sphere where the diameter is 12 inches.

Answer: 904.8

Question 3: A sphere has a radius of 3 units. Calculate its volume.

Answer: 113.1

Question 4: Construct a sphere with a radius of 4 cm and calculate its volume. Show your working.

Answer: 268.1

Question 1: A globe has a radius of 15 cm. Calculate its volume. If the globe's radius is increased by 10 cm, what is the new volume? Explain the impact of the change.

Answer: Original: 14137.2 cm³; New: 37700.8 cm³; The increase in radius causes a much larger increase in volume due to the r³ relationship.

Question 2: Explain why doubling the radius of a sphere results in an eightfold increase in volume. Support your explanation with calculations.

Answer: Volume ∝ r³; doubling r (2r) gives volume = ⁴⁄₃π(2r)³ = 8 * ⁴⁄₃πr³.

Question 1: A sports stadium uses a large spherical tank with a radius of 7 meters to store water. Calculate the volume of water it can hold.

Answer: 1436.8

Question 2: A science lab needs a spherical container with a volume of approximately 500 liters. What should be the radius of the sphere? (1 liter = 1000 cm³).

Answer: 4.4

Question 1: A sphere's volume is 1000 cm³. Find its radius. Show all steps.

Answer: 6.2

Question 2: Compare the volumes of two spheres with radii 3 cm and 9 cm. Calculate the ratio of their volumes and explain the relationship.

Answer: 1:27

Question 1: A student calculated the volume of a sphere with radius 8 cm as 1600 cm³. Find the mistake and correct the calculation.

Answer: Incorrect; volume = ⁴⁄₃π(8)³ ≈ 2144.7 cm³.

Question 2: A common mistake is to forget the r³ term in the volume formula. Describe how this mistake affects the calculation and the importance of cubic relationships.

Answer: Forgetting r³ leads to underestimating volume; the cubic relationship means larger radii increase volume exponentially.