Surface Areas and Volumes

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13 Surface Areas and Volumes

SURFACE AREAS AND VOLUMES

Cube:

Side of cube is ‘a’.

L a t e r a l s u r f a c e a r e a o f c u b e = 4 a^{2}

T o t a l s u r f a c e a r e a = 6 a^{2}

Cuboid:

The length of cuboid = 1,

Breadth = b

Height = h.

Lateral surface area of cuboid = 2(1h + bh)

= 2h(1+b)

Total surface area of cuboid = 2(1b + bh + 1h)

Right circular cylinder:

Base radius = r

Height = h

L a t e r a l s u r f a c e a r e a o f c y l i n d e r = 2 πrh

T o t a l s u r f a c e a r e a o f c y l i n d e r = 2 πr (r + h)

Right circular cone:

Base radius = r

Height = h

Slant height = 1

L a t e r a l s u r f a c e a r e a o f c o n e = πr 1

T o t a l s u r f a c e a r e a o f c o n e = πr (r + 1)

Sphere:

R a d i u s = r S u r f a c e a r e a = 4 {πr}^{2}

Hemisphere:

L a t e r a l s u r f a c e a r e a = 2 {πr}^{2}

T o t a l s u r f a c e a r e a = 2 {πr}^{2} + {πr}^{2}

= 3 {πr}^{2}

VOLUMES

V o l u m e o f C u b e = a^{3}

V o l u m e o f C u b o i d = 1 b h

V o l u m e o f R i g h t c y l i n d e r = {πr}^{2} h

V o l u m e o f C o n e = \frac{1}{3} {πr}^{2} h

Volume of Sphere = \frac{4}{3} {πr}^{3}

V o l u m e o f H e m i s p h e r e = \frac{2}{3} {πr}^{3}

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Number System

Polynomials

Coordinate geometry

Linear equations in two variables

Introduction to Euclid’s geometry

Lines and angles

Triangles

Quadrilaterals

Areas of parallelogram

Circles

Constructions

Heron’s formula

Statistics

Probability

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