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Directions for Questions 65–67: A man goes to a shop from his home at a speed of _____ km/h, and the time taken to reach the shop is _____ hours. After reaching there, he purchases a cylindrical jar of height such that its capacity is \(83259\text{ cm}^3\). He also purchases a conical vessel whose capacity is \(\frac{1}{27}\) of the cylindrical jar, and the height of the conical vessel is 14 cm. Note: The height of the conical vessel is four times the height of the cylindrical jar. Find the ratio of the radius of the cylindrical jar to the radius of the conical vessel.

1. 3:1
2. 4:1
3. 5:1
4. 6:1

Correct answer: 4:1

Solution

The cone’s height is four times the cylinder’s height, so the cylinder height is \(14/4 = 3.5\) cm. Using \(V=\pi r^2 h\) for the cylinder and \(V=\frac{1}{3}\pi r^2 h\) for the cone, along with the volume ratio \(1:27\), the radii ratio simplifies to \(4:1\).

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