Question

The volume V of liquid inside a conical tank of radius r₁ is related to the depth h of liquid by V = (1/3)π(r₁² + r₁r₂ + r₂²)h. If r₁ = 5 ft and r₂ = 2 ft, find the volume V when the depth h is 8 ft.

Answer 1

The volume of the liquid in the conical tank is approximately 326.725 ft³.

Step-by-step explanation:

The formula for the volume V of liquid inside a conical tank is given by:

V = (1/3)π(r₁² + r₁r₂ + r₂²)h

Given that r₁ = 5 ft, r₂ = 2 ft, and h = 8 ft, we can substitute these values into the formula:

V = (1/3)π((5 ft)² + (5 ft)(2 ft) + (2 ft)²)(8 ft)

Simplifying the expression inside the parentheses:

V = (1/3)π((25 ft²) + (10 ft²) + (4 ft²))(8 ft)

V = (1/3)π((39 ft²))(8 ft)

V = (1/3)(3.1416)((39 ft²))(8 ft)

V ≈ 326.725 ft³