Surface Area of Sphere MCQs Quiz | Class 9
Welcome to the Class IX Mathematics (Code 041) practice session for Unit V: Mensuration. This quiz specifically covers the Topic: Surface Area of Sphere MCQs Quiz | Class 9, focusing on the Surface area formula and its applications. Test your understanding of how to calculate the surface area of spheres and hemispheres. Once completed, click ‘Submit Quiz’ to view your score and use the ‘Download Answer PDF’ feature to save your results for offline revision.
Overview: Surface Area of Spheres and Hemispheres
In Mensuration, a sphere is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball. Like a circle in a two-dimensional space, a sphere is defined mathematically as the set of points that are all at the same distance r from a given point in a three-dimensional space.
Key Formulas
It is essential to memorize the specific formulas for spheres and hemispheres (half-spheres). Remember that “pi” is approximately 22/7 or 3.14.
| Shape | Dimension | Formula |
|---|---|---|
| Sphere | Surface Area (SA) | 4 x pi x r^2 |
| Hemisphere | Curved Surface Area (CSA) | 2 x pi x r^2 |
| Hemisphere | Total Surface Area (TSA) | 3 x pi x r^2 |
Important Concepts
- Radius vs Diameter: Always check if the question gives the diameter (d). If so, calculate radius (r = d/2) before using the formula.
- Units: Surface area is always measured in square units (e.g., cm^2, m^2). Ensure all dimensions are in the same unit before calculating.
- Solid vs Hollow: For a solid hemisphere, the Total Surface Area includes the curved part plus the flat circular base (2 pi r^2 + pi r^2 = 3 pi r^2). For a hollow hemisphere open at the top, we usually consider only the Curved Surface Area.
Quick Revision Notes
1. If the radius of a sphere is doubled, its surface area becomes 4 times the original area.
2. The surface area of a sphere is equal to the curved surface area of a cylinder that circumscribes the sphere (where cylinder height = 2r and cylinder radius = r).
3. When painting a hemispherical dome, use the CSA formula. When polishing a solid hemispherical paperweight, use the TSA formula.
Extra Practice Questions
- Find the surface area of a sphere of diameter 21 cm. (Ans: 1386 cm^2)
- A hemispherical bowl represents a CSA calculation. If radius is 3.5 cm, find the CSA. (Ans: 77 cm^2)
- If the surface area of a sphere is 616 cm^2, find its radius. (Ans: 7 cm)
- Find the ratio of surface areas of two spheres with radii 2 cm and 3 cm. (Ans: 4:9)
- Calculate the total surface area of a solid hemisphere of radius 10 cm. (Use pi=3.14). (Ans: 942 cm^2)
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