Chapter 13 Surface Areas and Volumes

Notes

Surface Areas and Volumes:

This chapter deals with area covering the outer surface and space occupied by solids.

Important Solids:

Cube Cuboid Cylinder Cone Sphere Hemisphere

Cube:

V=a 3 s V=s 3 ≈27.00 s = 3 Total Surface Area = 6a²

Cuboid: V=lbh

Total Surface Area = 2(lb + bh + hl)

Cylinder:

V=πr 2 h r h A base ​

=πr 2 ≈28.27 V=πr 2 h≈226.19 r = 3.0 h = 8.0 Curved Surface Area = 2πrh

Cone:

V= 3 1 ​

πr 2 h r h A base ​

=πr 2 ≈28.27 V= 3 1 ​

πr 2 h≈75.40 r = 3.0 h = 8.0 Curved Surface Area = πrl Slant Height: l = √(r² + h²)

Sphere:

V= 3 4 ​

πr 3 r V= 3 4 ​

πr 3 ≈113.10 r = 3.0 Surface Area = 4πr²

Hemisphere:

Volume = 2/3 πr³ CSA = 2πr² TSA = 3πr²

Important Points:

Use π = 22/7 unless otherwise given Convert diameter to radius first Always write units

Common Mistakes:

Forgetting 1/3 in cone Using diameter directly Confusing CSA and TSA