Surface Areas and Volumes: Class 10 Mathematics Q&A
4 free answers on Surface Areas and Volumes (Mathematics) for Class 10 students, across CBSE, ICSE and State boards. Includes questions such as “What is the TSA formula for a hollow sphere”, “Why are CSA and TSA of sphere the same”, “How to calculate cross sectional area of sphere”.
Question & Answer
Questions
- MathematicsClass 10All
What is the TSA formula for a hollow sphere
The Total Surface Area (TSA) formula for a hollow sphere (spherical shell) with inner radius r₁ and outer radius r₂ is TSA = 4πr₂² + 4πr₁² = 4π(r₂² + r₁²), which accounts for both the outer sphere surface and the inner sphere surface. This formula recognizes that a hollow sphere has two distinct surfaces requiring measurement—the larger outer surface and the smaller inner surface—and TSA includes both since they're both part of the object's complete bo
- MathematicsClass 10All
Why are CSA and TSA of sphere the same
The CSA (Curved Surface Area) and TSA (Total Surface Area) of a sphere are identical because a sphere consists entirely of one continuous curved surface with absolutely no flat surfaces, edges, bases, or caps—there are no additional surfaces to add when calculating total surface area. Unlike cylinders (which have flat circular ends), cones (which have flat circular bases), or prisms (which have flat faces), a sphere is pure curved surface extending uniformly in all directions from its c
- MathematicsClass 10All
How to calculate cross sectional area of sphere
The cross-sectional area of a sphere taken through any plane passing through or intersecting the sphere depends on where the cut is made. The maximum cross-sectional area occurs when cutting through the sphere's center (equatorial cut), producing a circle with radius equal to the sphere's radius r, giving a cross-sectional area of πr²—the area of the largest possible circular slice. Cuts made at other positions (not through center) produce smaller circular cross-sections with ra
- MathematicsClass 10All
What is the CSA of a spherical shell
A spherical shell (hollow sphere with inner radius r₁ and outer radius r₂) has two curved surfaces—the outer sphere surface and the inner sphere surface—making the total CSA = 4πr₂² + 4πr₁², which can be factored as 4π(r₂² + r₁²). This formula adds the surface area of the larger outer sphere (4πr₂²) and the smaller inner sphere (4πr₁²) since both surfaces exist and contribute to the total curved surface area of the hollow shell. <p