A cube and cuboid have the same base area. The volume of the cube is 64cm$^3$ while that of the cuboid is 80cm$^3$. Find the height of the cuboid

Analyze the question: A cube and a cuboid share the same base area. We know both volumes and need the cuboid's height.

Concept:

• Volume of cube = side³
• Volume of cuboid = base area × height

Step 1: Find the side of the cube s³ = 64, so s = ∛64 = 4 cm

Step 2: Find the base area Base area = s² = 4 × 4 = 16 cm²

Step 3: Find the cuboid's height Volume = base area × height 80 = 16 × h h = 80 ÷ 16 = 5 cm

Answer: C. 5 cm

Tip: When two solids share a base area, you can also use a shortcut: the heights are in the ratio of their volumes. The cube's height is 4, so the cuboid's height = 4 × (80/64) = 5 cm. Memorize common cube roots (8 → 2, 27 → 3, 64 → 4, 125 → 5) to save time in the exam.