The church steeple is a frustum, and the volume of the church steeple is 107.5 ft³
How to determine the volume of the steeple?
The given parameters are:
- Height, h = 30 feet
- Base length, L = 3 feet
- Top length, l = 6 inches
Calculate the base area:
A₁ = L²
This gives
A₁ = (3 ft)²
A₁ = 9 ft²
Calculate the top area:
A₂ = l²
This gives
A₂ = (6 in)²
Express inches as feet
A₂ = (6/12 ft)²
A₂ = (0.5 ft)²
Evaluate the square
A₂ = 0.25 ft²
The volume of the church steeple is then calculated using:
[tex]V = \frac h3 * (A_1 + A_2 + \sqrt{A_1 * A_2})[/tex]
This gives
[tex]V = \frac {30}3 * (9 + 0.25 + \sqrt{9 * 0.25})[/tex]
Evaluate the product, the sum and the quotient
[tex]V = 10 * (9.25 + \sqrt{2.25})[/tex]
Evaluate the exponent
[tex]V = 10 * (9.25 + 1.5)[/tex]
Evaluate the product
V = 107.5
Hence, the volume of the church steeple is 107.5 ft³
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