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