The volume of a pyramid with height 15cm is 90cm3. If its base is a rectangle with dimension xcm by 6cm, find the value of x

Analyze the question: We have a pyramid with a rectangular base (x cm by 6 cm), a height of 15 cm, and a volume of 90 cm³. We need to find x.

Concept: The volume of a pyramid is

V = (1/3) × (base area) × height

For a rectangular base, base area = length × width = x × 6.

Solution:

1. Write the formula: 90 = (1/3) × (x × 6) × 15

2. Simplify the right-hand side: (1/3) × 6 × 15 = 30, so 90 = 30x

3. Solve for x: x = 90 ÷ 30 = 3

Check: Base area = 3 × 6 = 18 cm². Volume = (1/3) × 18 × 15 = 90 cm³ ✔

So x = 3 cm, which is option A.

Tip: For pyramids and cones, always remember the factor 1/3. Prisms and cuboids don't have it, but pyramids and cones do. In "find the missing side" questions, put the numbers into the formula first and simplify before solving. Here, (1/3) × 6 × 15 = 30 made the algebra very quick.