Surface Areas and VolumesPractice Questions & MCQs

Q1. If the height of a cylinder is doubled and the radius is tripled, the new volume becomes how many times the original volume?

• A.18
• B.12
• C.6
• D.9

Answer: A. 18

What does the chapter say about this? V ∝ r^2 h → factor (3)^2·2 = 18. Trap: adding factors 9+2 = 11. Pick: A) 18.

Q2. If the radius and the height of a right circular cylinder are each tripled, the new volume is what multiple of the original volume?

• A.27
• B.9
• C.3
• D.12

Answer: A. 27

Q3. A cube of edge 12 cm is cut by three mutually perpendicular cuts through its centre, producing 8 identical smaller cubes. By what percentage does the combined surface area of the 8 pieces exceed the surface area of the original cube?

• A.100%
• B.50%
• C.200%
• D.300%

Answer: A. 100%

Diagnose the question type - a typical math numerical. The data on the table: 12 cm. We are after the quantity the stem asks for. Tool of choice - Original TSA = 6·144 = 864 cm^2. Rearrange it for the unknown before substituting. Numbers in: Original TSA = 6·144 = 864 cm^2 → Each small cube has edge 6, TSA = 216 → eight together = 1728 → Increase = 864, percentage = 100%. Common-sense check: Trap: comparing one small-cube TSA to the big-cube TSA. Lock in option A) 100%.