The Sphere

The Cone

Any Prisms

Volume of SolidsVolume of Solidsw

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Composite Prisms

StarterStarter

1. Calculate the area of the following shapes.

2. Round to 3 sig. figures.

(a) 47856 (b) 0.065797 (c) 2.05700

Q3. Find 30% of £ 360

5 cm

2.5 cm3 cm

4 cm

3 cm

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Volume of a Sphere

34Volume = πr

3

1r = radius = D

2

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r

D

D = diameter

Q. If the above sphere has radius 10cm. Calculate it’s volume.

3 34Volume = π(10) =4187cm ( to 4 sig. figs)

3

StarterStarter

Q1. Calculate the volume of the following sphere.

Q2. Car depreciates 10% each year. What is

it's value after 3 years if it's initial value was £3,000.

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D = 6 cm

r

D

4 3Volume = πr34 3 = π(3)3

3 = 36πcm

Q. If the above cone has radius 15cm and heightof 10 cm. Calculate it’s volume.

Volume of a Cone

h = Perpendicular height

2 31Volume = π(15) 10 = 2355cm

3

r = radius

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r

h21

Volume Cone = πr h3

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Definition : A prism is a solid shape with uniform cross-section

Cylinder(circular Prism) Pentagonal PrismTriangular Prism

Hexagonal Prism

Volume = Area of Cross section x length

Volume of SolidsVolume of Solids

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Definition : A prism is a solid shape with uniform cross-section

Triangular PrismVolume = Area x length

Q. Find the volume the triangular prism.

20cm210cm= 20 x 10 = 200 cm

3

Volume of SolidsVolume of Solids

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Definition : A prism is a solid shape with uniform cross-section

Volume = Area x length

Q. Find the volume the hexagonal prism.43.2cm

2

20cm

= 43.2 x 20 = 864 cm3 Hexagonal Prism

Volume of SolidsVolume of Solids

Q1. Calculate the volume of the following cone.

Q2. My wages increased by 10% this year. My new wage

is £1200. What was my wage before the increase.

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D = 6 cm

h = 10 cm

r

h

2

2

3

1Volume Cone = πr h

31

= π(3) ×10 3

= 30 cm

Volume of a SolidVolume of a Solid

21Volume Cone = πr h

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Composite volume is simply volumes that are made up from basic volumes.

r

D

r

h

Volume = Area x length

34Volume = πr

3

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Q. Find the volume the composite shape.

Composite volume is simply volumes that are made up from basic volumes.

Volume = Cylinder + half a sphere

h = 6m r2m

2

2

3

V=πr h

=π(2) 6

=24π m

3

3

3

1 4V= ( πr )

2 31 4

= ( π(2) )2 316

= π m3

316 88Total 24 = π = 92.15m

3 3

½ sphereCylinder

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Q. This child’s toy is made from 2 identical cones. Calculate the total volume.

Composite Volumesare simply volumes that are made up from basic volumes.

Volume = 2 x cone

2

2

3

1V = πr h

31

= π (10) 303

= 3141.5cm

r = 10cm

h = 60cm

One cone

Two cone 3 = 2 3141.5 = 6283cm