Right Circular Cone: Volume MCQs Quiz | Class 9
Class: IX | Subject: Mathematics (Code 041) | Unit: Unit V: Mensuration | Topic: Right Circular Cone: Volume | Covering: Volume formula; applications. Instructions: Select the best answer for each question. Click Submit to view results and download the solution PDF.
Overview: Volume of a Right Circular Cone
In Class IX Mathematics, Unit V (Mensuration), understanding the volume of a right circular cone is essential. A cone is a three-dimensional shape that tapers smoothly from a flat base (usually circular) to a point called the apex or vertex. The volume of a cone is directly related to the volume of a cylinder with the same base radius and height.
Key Formula
The volume (V) of a right circular cone is given by the formula:
V = (1/3) pi r^2 h
- pi: The constant approx. 22/7 or 3.14
- r: Radius of the circular base
- h: Perpendicular height of the cone
Note: The volume of a cone is exactly one-third the volume of a cylinder with the same dimensions.
Comparison Table
| Solid | Volume Formula | Relationship |
|---|---|---|
| Cylinder | pi r^2 h | Base unit |
| Cone | (1/3) pi r^2 h | 1/3 of Cylinder |
Quick Revision Points
- If the radius of a cone is doubled (keeping height constant), the volume becomes 4 times the original.
- If the height is doubled (keeping radius constant), the volume doubles.
- Always ensure units are consistent (e.g., all in cm or all in m) before calculating.
- 1000 cubic cm = 1 Liter.
Extra Practice Questions
- Find the volume of a cone if radius = 6 cm and height = 7 cm. (Answer: 264 cubic cm)
- If the volume of a cone is 1570 cubic cm and the base area is 314 sq cm, find its height. (Answer: 15 cm)
- A conical pit of top diameter 3.5 m is 12 m deep. What is its capacity in kiloliters? (Answer: 38.5 kl)
- Find the volume of a right circular cone with height 21 cm and slant height 28 cm. (Answer: approx 7546 cubic cm)
- If both radius and height of a cone are doubled, how many times does the volume increase? (Answer: 8 times)
