Chapter 12: Surface Areas and Volumes

Refined and Comprehensive Class 10 Mathematics Notes

Important Formulas

1. Cylinder

CSA = 2πrh
TSA = 2πr(h + r)
V = πr²h

2. Cone

Slant Height (l) = √(r² + h²)
CSA = πrl
V = ⅓πr²h

3. Sphere

SA = 4πr²
V = ⁴⁄₃πr³

4. Hemisphere

CSA = 2πr²
TSA = 3πr²
V = ⅔πr³

Points to Remember

Volume Conservation: When a solid of one shape is melted and recast into another shape, its total volume remains unchanged (Volume before recasting = Volume after recasting).
Combined Surface Area: The total surface area of a combined solid is the sum of the curved surface areas of its individual visible parts, NOT the sum of their total surface areas.

Important Practice Questions

  1. Find the total volume of a combined solid formed by two or more 3D shapes.
  2. A metallic solid is melted and recast into another shape; calculate the new dimensions or quantity of recast items.
  3. Find the surface area of a composite object made by joining two or more solids.

Quick Revision

Cylinder Volume

V = πr²h

Cone Slant Height

l = √(r² + h²)

Sphere Surface Area

SA = 4πr²

Hemisphere TSA

TSA = 3πr²