Question

What is the volume of a 6 m deep tank having rectangular shaped top 6 m $\times$ 4 m and bottom 4 m $\times$ 2 m? (use mean-area method)

• A. 92 m$^3$
• B. 94 m$^3$
• C. 96 m$^3$
• D. 90 m$^3$

Hint:

Use the mean-area method for trapezoidal cross-section tanks to calculate volume.

Answer 1

The Correct Option is A

Step 1: Mean Area Metho(D)
The volume of the trapezoidal tank can be calculated using the mean area metho(D) The formula is: \[ V = h \times \left( \frac{A_1 + A_2}{2} \right) \] Where: - \(h\) = height of the tank = 6 m - \(A_1\) = area of the top = \(6 \times 4 = 24 \, \text{m}^2\) - \(A_2\) = area of the bottom = \(4 \times 2 = 8 \, \text{m}^2\)
Step 2: Calculating Volume.
\[ V = 6 \times \left( \frac{24 + 8}{2} \right) = 6 \times 16 = 96 \, \text{m}^3 \] Thus, the correct volume is \( 96 \, \text{m}^3 \), so option (3) is correct.

Final Answer: \[ \boxed{96 \, \text{m}^3} \]