The dimension of a rectangular base of a right pyramid is 9 cm by 5cm. If the volume of the pyramid is 105 cm$^3$, how high is the pyramid?

Analyze the question: We have a right pyramid with a rectangular base of 9 cm by 5 cm and volume 105 cm³. We need to find its height.

Concept: The volume of any pyramid is

V = (1/3) × (base area) × height

Solution:

1. Base area = 9 × 5 = 45 cm²

2. Substitute into the formula: 105 = (1/3) × 45 × h

3. Simplify: 105 = 15h

4. Solve for h: h = 105 ÷ 15 = 7 cm

Check: (1/3) × 45 × 7 = 15 × 7 = 105 cm³ ✓

Tip: For pyramids and cones, always remember the factor of 1/3. If you forget it, you'd get h = 105 ÷ 45 ≈ 2.33, which isn't among the options, a quick signal that something is missing. Also, you can multiply the volume by 3 first (105 × 3 = 315) and then divide by the base area (315 ÷ 45 = 7), which is often quicker.