A cylindrical tank has a capacity of 3080m3. What is the depth of the tank if the diameter of its base is 14m? Take pi = 22/7.

1. Analyze the Question

We are given the volume (capacity) of a cylindrical tank and the diameter of its base. We need to find the depth (height) of the tank.

• Volume ($V$): $3080 \, \text{m}^3$
• Diameter ($d$): $14 \, \text{m}$
• $\pi$: $22/7$
• Find: Height ($h$)

2. Explain the Concept

A cylinder's volume is calculated using the formula:

Where:

• $r$ is the radius of the base.
• $h$ is the height (or depth) of the cylinder.

Since we are given the diameter, we must first find the radius. Remember that the radius is half of the diameter ($r = d / 2$).

3. Show the Solution

Step 1: Find the radius ($r$)

Step 2: Substitute the known values into the volume formula

Step 3: Simplify the equation

Divide 49 by 7:

Step 4: Solve for $h$

4. Identify the Answer

Comparing our result to the given options, the correct answer is 20m, which corresponds to option C.

5. Exam Tip

When dealing with geometry problems involving $\pi = 22/7$, always look for ways to cancel out the denominator early. Notice how the $7$ in the denominator canceled out perfectly with the $7^2$ (which is $7 \times 7$), making the multiplication much easier and faster for your JAMB exam!