Example (1): A pyramid with a square base

• A pyramid has a square base of side 6 cm and height 4 cm. Find its volume.
• Solution:

1. Area of the base = 6² = 36 cm².
2. Volume = ⅓ × 36 × 4 = 48 cm³.

Example (2): A pyramid with a rectangular base

• A pyramid has a rectangular base with sides 8 cm and 5 cm, and height 9 cm. Find its volume.
• Solution:

1. Area of the base = 8 × 5 = 40 cm².
2. Volume = ⅓ × 40 × 9 = 120 cm³.

Example (3): A right circular cone

• A right circular cone has base radius 3 cm and height 4 cm.
• Find its volume in terms of π, then round the answer to two decimal places.
• Solution:

1. Volume = ⅓ × π × 3² × 4 = ⅓ × 36π = 12π cm³.
2. 12π ≈ 37.70 cm³.

Example (4): Finding the height from the slant height

• A right circular cone has base radius 5 cm and slant height 13 cm. Find its volume in terms of π.
• Solution:

1. h² = 13² − 5² = 144, so h = 12 cm.
2. Volume = ⅓ × π × 5² × 12 = ⅓ × 300π = 100π cm³.
3. 100π ≈ 314.16 cm³.

Example (5): A pyramid with an equilateral triangular base

• A pyramid has an equilateral triangular base of side 6 cm and height 6 cm. Find its volume.
• Solution:

1. Area of the base = √3 ÷ 4 × 6² = 9√3 cm².
2. Volume = ⅓ × 9√3 × 6 = 18√3 ≈ 31.18 cm³.