Question 1: Calculate the surface area of a sphere with a radius of 7 cm. Use π ≈ 3.14.

Answer: 1538.56

Question 2: Find the volume of a sphere with a diameter of 10 meters. Use π ≈ 3.14.

Answer: 523.33

Question 3: A ball has a radius of 4 inches. Calculate its surface area.

Answer: 201.06

Question 4: Plot the graph of y = 2x on the grid, representing a relationship involving sphere measurements.

Answer:

Question 5: Construct a sphere with a radius of 5 cm using the grid to visualize the shape.

Answer:

Question 6: Given a sphere with surface area 315.68 cm², find its radius (π ≈ 3.14).

Answer: 5 cm

Question 7: A spherical tank has a volume of 4188.8 liters. What is its radius in meters? (1 liter = 1000 cm³, use π ≈ 3.14).

Answer: ≈ 3 m

Question 8: Explain why the surface area of a sphere increases faster than its volume as the radius increases.

Answer: Surface area is proportional to r², while volume is proportional to r³, so as r increases, volume grows faster, but surface area increases at a different rate.

Question 9: A sphere's surface area is 615.75 cm². If the radius is doubled, what will be the new surface area?

Answer: 2463.00

Question 10: Identify and correct the mistake: A student calculates the volume of a sphere with radius 6 cm using V = (4/3)πr³ and gets 904.8 cm³. (Use π ≈ 3.14).

Answer: Correct calculation is V = (4/3)×3.14×6³ ≈ 904.78 cm³; the student's answer is correct, but rounding may differ slightly.

Question 11: Challenge: Derive a formula for the surface area of a sphere in terms of its volume, and verify it with the known formulas.

Answer: Surface area S = 4πr², volume V = (4/3)πr³, so r = (3V/4π)^(1/3); substituting r back gives S in terms of V.