Learning Objectives
- Calculate surface areas of cubes, cuboids, cylinders, cones, and spheres
- Calculate volumes of cubes, cuboids, cylinders, cones, and spheres
- Distinguish between lateral/curved surface area and total surface area
- Solve problems involving combinations of solids
Key Concepts
Cuboid (l × b × h)
Lateral Surface Area: 2h(l + b)
Total Surface Area: 2(lb + bh + hl)
Volume: l × b × h
Cube (side = a)
Lateral Surface Area: 4a²
Total Surface Area: 6a²
Volume: a³
Right Circular Cylinder (radius r, height h)
Curved Surface Area: 2πrh
Total Surface Area: 2πr(r + h)
Volume: πr²h
Right Circular Cone (radius r, height h, slant height l)
Slant height: l = √(r² + h²)
Curved Surface Area: πrl
Total Surface Area: πr(l + r)
Volume: (1/3)πr²h
Sphere (radius r)
Surface Area: 4πr²
Volume: (4/3)πr³
Hemisphere (radius r)
Curved Surface Area: 2πr²
Total Surface Area: 3πr² (curved + base)
Volume: (2/3)πr³
Summary
This chapter covers the formulae for surface areas (both lateral and total) and volumes of five basic solids: cuboid, cube, cylinder, cone, and sphere, along with the hemisphere. The slant height of a cone is related to its radius and height by the Pythagorean relation. These formulae are fundamental for solving real-world measurement problems.
Important Terms
- Lateral Surface Area: The area of the sides only, excluding top and bottom
- Total Surface Area: The complete surface area including all faces
- Volume: The amount of space enclosed by a solid
- Slant Height: The distance along the surface of a cone from base to apex
Quick Revision
- Cube: TSA = 6a², Volume = a³
- Cuboid: TSA = 2(lb + bh + hl), Volume = lbh
- Cylinder: CSA = 2πrh, Volume = πr²h
- Cone: CSA = πrl, Volume = (1/3)πr²h, l = √(r² + h²)
- Sphere: SA = 4πr², Volume = (4/3)πr³
- Hemisphere: CSA = 2πr², Volume = (2/3)πr³