Nalanda College, Colombo 10 Grade 11 Maths Worksheet: 5 Volume of Solids

Volume of a square pyramid

Answer: 96 cm³

💡 What it's asking: A pyramid holds exactly one third of a prism with the same base and height. So find the base area first, then use V = 1/3 × base area × height.

1. 1The base is a square of side 6 cm, so its area is 6 × 6 = 36 cm².
2. 2Write the formula: V = 1/3 × base area × height.
3. 3Put in the numbers: V = 1/3 × 36 × 8.
4. 41/3 of 36 is 12, and 12 × 8 = 96, so V = 96 cm³.

✅ A box 6 × 6 × 8 would hold 288 cm³, and one third of 288 is 96, so the answer fits.

Pyramid volume in terms of a

Answer: 2a³/3 cm³

💡 What it's asking: Same pyramid formula, but with letters instead of numbers. Write the base area and height in terms of a, then multiply.

1. 1The base is a square of side a, so its area is a².
2. 2The height is 2a.
3. 3V = 1/3 × a² × 2a.
4. 4Multiply the letters: a² × a = a³, and 1/3 × 2 = 2/3, so V = 2a³/3 cm³.

✅ Try a = 3: base 9, height 6, V = 1/3 × 9 × 6 = 18, and 2 × 27 ÷ 3 = 18 too.