Question 1: Write down the formula for the surface area of a sphere in terms of its radius.

Answer: Surface Area = 4πr^2

Question 2: Calculate the surface area of a sphere with a radius of 5 cm.

Answer: 314.16

Question 3: Find the volume of a sphere with radius 3 meters. Use π ≈ 3.14.

Answer: 113.04

Question 4: A spherical ball has a diameter of 10 cm. Calculate its volume.

Answer: 523.33

Question 5: Explain why the surface area of a sphere increases faster than its volume as the radius increases.

Answer: Surface area increases proportional to r^2, while volume increases proportional to r^3, so volume grows faster as r increases.

Question 6: A sphere's surface area is 452.16 cm^2. Find its radius, taking π ≈ 3.14.

Answer: 6 cm

Question 7: A spherical tank has a radius of 8 meters. Calculate its volume and surface area.

Answer: Volume: 2144.66; Surface Area: 804.24

Question 8: A golf ball is a sphere with a diameter of 4.5 cm. Calculate the difference between the surface area and volume of the ball.

Answer: Surface area - Volume ≈ 33.5

Question 9: Construct a sphere on the grid with a radius of 3 units. Sketch the great circle on the surface.

Answer: Student draws a circle of radius 3 on the grid

Question 10: A spherical object has a surface area of 125.66 cm^2. Determine its radius.

Answer: r = 2 cm

Question 11: Identify and correct the mistake in this statement: 'The volume of a sphere is 4/3 π r^3, so doubling the radius doubles the volume.'

Answer: Doubling r increases volume by a factor of 8, not 2.

Question 12: A sphere's radius is increased from 4 cm to 6 cm. Calculate the percentage increase in surface area.

Answer: 58.14%