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Example 14 A frustum of a pyramid is 3 cm square at the and 6 cm square at the bottom and is 5 cm high. Calculate the volume of the frustum. top 1 xcm 3 cm 3 cm 5 cm For a ne of cm 6 cm ht is 6 cm​

Sagot :

183so2

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.

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