Find the volume of a cone which has a base radius of 5 cm and
MATHEMATICS
JAMB 2023
Find the volume of a cone which has a base radius of 5 cm and slant height of 13 cm.
- A. \(300\pi\) cm\(^2\)
- B. \(325\pi\) cm\(^2\)
- C. \(\frac{325}{3}\pi\) cm\(^2\)
- D. \(100\pi\) cm\(^2\)
Correct Answer: D. \(100\pi\) cm\(^2\)
Explanation
Volume of a cone = \(\frac{1}{3}\pi r^2 h\)
r = 5 cm
l = 13 cm
Using Pythagoras theorem
⇒ \(13^2 = 5^2 + h^2\)
⇒ \(169 = 25 + h^2\)
⇒ \(169 - 25 = h^2\)
⇒ \(h^2 = 144\)
⇒ \(h = \sqrt144 = 12 cm\)
∴ Volume of the cone = \(\frac{1}{3} \times\pi\times 5^2 x 12 = 100\pi\) cm\(^2\)
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