The volume of a cone (s) of height 6cm and base radius 5cm is

1. Analyze the question

We are asked to calculate the volume of a cone given its height ($h$) and base radius ($r$).

• Height ($h$) = 6 cm
• Radius ($r$) = 5 cm
• We will use $\pi \approx 3.142$ (standard for JAMB calculations unless specified as $22/7$).

2. Explain the concept

The volume ($V$) of a cone is given by the formula:

Where:

• $\pi$ (pi) is a constant (approximately 3.142 or 22/7)
• $r$ is the radius of the circular base
• $h$ is the perpendicular height of the cone

3. Show the solution

Step 1: Substitute the values into the formula.

Step 2: Simplify the expression. First, calculate the square of the radius:

Now, substitute back:

Step 3: Perform the arithmetic. You can simplify $\frac{1}{3} \times 6$ first, which equals 2:

Step 4: Calculate the final numerical value. Using $\pi \approx 3.14159...$

Rounding to the nearest whole number, we get 157 cm³.

4. Identify the answer

Comparing our result to the given options, it matches option A.

5. Tip

In JAMB Mathematics, if you see $\pi$ in the options, leave your answer in terms of $\pi$. If the options are whole numbers, use $3.142$ for $\pi$ to get the most accurate result. Also, remember that the volume of a cone is exactly one-third the volume of a cylinder with the same radius and height ($V_{cylinder} = \pi r^2 h$).