Find the volume of a cone which has a base radi... - JAMB Mathematics 2023 Question

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

\[V = \frac{1}{3} \pi r^2 h\]

where:
- \(\pi\) is a mathematical constant approximately equal to 3.14159,
- \(r\) is the radius of the base of the cone,
- \(h\) is the height of the cone.

Given that the base radius (\(r\)) is 5 cm and the slant height is the hypotenuse of the right triangle formed by the radius, and the height (\(h\)) can be found using the Pythagorean theorem:

\[h = \sqrt{\text{{slant height}}^2 - \text{{radius}}^2}\]

Substitute the values into the formula for the volume:

\[V = \frac{1}{3} \pi (5)^2 \sqrt{13^2 - 5^2}\]

Let's calculate this to find the correct volume.

\[h = \sqrt{13^2 - 5^2} = \sqrt{169 - 25} = \sqrt{144} = 12 \, \text{cm}\]

Now, substitute the values into the formula for the volume:

\[V = \frac{1}{3} \pi (5)^2 \times 12 = \frac{1}{3} \pi \times 25 \times 12 = 100 \pi \, \text{cm}^3\]