Volume of Sphere MCQs Quiz | Class 9
This Class IX Mathematics (Code 041) quiz covers Unit V: Mensuration, specifically focusing on the Volume of Sphere. Topics include the volume formula, calculations involving radius and diameter, and real-life applications. Test your understanding, view your score immediately, and click “Download Answer PDF” to save your results for offline revision.
Overview of Sphere Mensuration
In Class 9 Mathematics, Mensuration involves studying geometric shapes and their parameters like volume and surface area. The sphere is a perfectly round 3D object where every point on the surface is equidistant from the center. Understanding the volume of a sphere is crucial for solving problems related to capacity, displacement, and material requirements.
Key Formulas
The primary formula for the volume of a sphere depends on its radius (r). If the diameter (d) is given, remember that radius is half of the diameter (r = d/2).
| Shape | Parameter | Formula |
|---|---|---|
| Sphere | Volume | (4/3) x pi x r^3 |
| Hemisphere | Volume | (2/3) x pi x r^3 |
Common Applications
- Recasting: Melting a large metal sphere to form smaller spheres. The total volume remains constant.
- Displacement: Calculating the rise in water level when a spherical object is submerged.
- Capacity: Finding how much liquid a hemispherical bowl can hold.
Quick Revision Points
- Unit Consistency: Always ensure radius and volume are in consistent units (e.g., cm and cubic cm).
- Value of Pi: Use 22/7 or 3.14 as specified. If not specified, 22/7 is standard.
- Cubic Units: Volume is always measured in cubic units (cm^3, m^3).
Extra Practice Questions
1. A sphere has a radius of 7 cm. Find its volume using pi = 22/7.
2. How many lead shots of radius 1 cm can be made from a sphere of radius 4 cm?
3. The diameter of a metallic ball is 4.2 cm. What is the mass of the ball, if the density of the metal is 8.9 g per cm cube?
4. Find the volume of a hemisphere of radius 3.5 cm.
5. If the volume of a sphere is numerically equal to its surface area, what is its radius?
