Answer:
The volume of a frustum of a pyramid can be calculated using the formula:
V = (1/3) h (A + √(A*a) + a)
where:
- V is the volume of the frustum
- h is the height of the frustum
- A is the area of the base (larger base)
- a is the area of the top (smaller base)
Given:
- Top base edge length = 3 cm
- Bottom base edge length = 6 cm
- Height = 5 cm
Step 1: Calculate the area of the top base (smaller base)
A_top = 3 cm × 3 cm = 9 cm²
Step 2: Calculate the area of the bottom base (larger base)
A_bottom = 6 cm × 6 cm = 36 cm²
Step 3: Calculate the volume using the formula
V = (1/3) × 5 cm × (36 cm² + √(36 cm² × 9 cm²) + 9 cm²)
V = (1/3) × 5 cm × (36 + √324 + 9)
V = (1/3) × 5 cm × (36 + 27 + 3)
V = (1/3) × 5 cm × 66
V = 110 cm³
Therefore, the volume of the frustum is 110 cm³.
