Surface Areas and Volumes — Important Questions

3053.6 cm³

Step 1: Given radius r = 9 cm. Step 2: For a sphere, volume = (4/3)πr³. Step 3: Substitute values: Volume = (4/3) × (22/7) × 9³ = (4/3) × (22/7) × 729. Step 4: Calculate: Volume = (4 × 22 × 729)/(3 × 7) = 64152/21 = 3053.6 cm³. Remember to cube the radius first.

754.3 cm³

Step 1: Given radius r = 4 cm and height h = 15 cm. Step 2: For a cylinder, volume = πr²h. Step 3: Substitute values: Volume = (22/7) × 4² × 15 = (22/7) × 16 × 15. Step 4: Calculate: Volume = (22 × 240)/7 = 5280/7 = 754.3 cm³. The volume is the area of the circular base times the height.

301.7 cm³

Step 1: Given radius r = 6 cm and height h = 8 cm. Step 2: For a cone, volume = (1/3)πr²h. Step 3: Substitute values: Volume = (1/3) × (22/7) × 6² × 8 = (1/3) × (22/7) × 36 × 8. Step 4: Calculate: Volume = (22 × 288)/(3 × 7) = 6336/21 = 301.7 cm³. Cone volume is one-third of cylinder volume with same base and height.

244.3 cm²

Step 1: Both shapes have radius r = 3 cm, cylinder height h = 10 cm. Step 2: Total surface area = CSA of hemisphere + CSA of cylinder + base area of cylinder. Step 3: Calculate each part: CSA of hemisphere = 2πr² = 2 × (22/7) × 9 = 56.6 cm²; CSA of cylinder = 2πrh = 2 × (22/7) × 3 × 10 = 188.6 cm²; Base area = πr² = (22/7) × 9 = 28.3 cm². Step 4: Add them: 56.6 + 188.6 + 28.3 = 244.3 cm². Note: The hemisphere covers one base of the cylinder.