Transcript Volume of Prisms

Volume of Solids
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Int 2
The Sphere
The Cone
Any Prisms
Composite Prisms
Starter
Int 2
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1.
Calculate the area of the following shapes.
5 cm
2.5 cm
2.
3 cm
3 cm
4 cm
Round to 3 sig. figures.
(a) 47856
(b) 0.065797
Q3. Find 30% of £360
(c) 2.05700
Volume of Solids
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Int 2
Learning Intention
1. To understand the
sphere formula and use it
appropriately.
Success Criteria
1. To know the volume
formula for a sphere.
2. Work out volumes for
spheres.
3. Answer to contain
appropriate units and
working.
Volume of a Sphere
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Int 2
r
D
Q.
D = diameter
1
r = radius = D
2
4 3
Volume = πr
3
If the above sphere has radius 10cm.
Calculate it’s volume.
4
Volume = π(10)3=4187cm3 ( to 4 sig. figs)
3
Volume of Solids
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Int 2
Now try MIA Ex 1
Ch3 (page 20)
Starter
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Int 2
Q1.
Calculate the volume of the following sphere.
4 3
Volume = πr
3
4
= π(3)3
3
= 36πcm 3
Q2.
r
D = 6 cm
D
Car depreciates 10% each year. What is
it's value after 3 years if it's initial value was £3,000.
Volume of Solids
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Int 2
Learning Intention
1. To understand the
cone formula and use it
appropriately.
Success Criteria
1. To know the volume
formula for a cone.
2. Work out volumes for
various cones.
3. Answer to contain
appropriate units and
working.
Volume of a Cone
Int 2
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r = radius
h = Perpendicular height
h
r
1 2
Volume Cone = πr h
3
Q. If the above cone has radius 15cm and height
of 10 cm. Calculate it’s volume.
1
Volume = π(15)2  10 = 2355cm3
3
Volume of Solids
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Int 2
Now try MIA Ex 2
Ch3 (page 22)
Starter
Int 2
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1.
Calculate the area of the following shapes.
r = 3cm
2.
6 cm
5 cm
8 cm
6 cm
Round to 3 sig. figures.
(a) 47856
(b) 0.065797
Q3. Find 30% of £360
(c) 2.05700
Volume of Solids
Prisms
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Int 2
Learning Intention
1. To understand the
prism formula for
calculating volume.
Success Criteria
1. To know the volume
formula for any prism.
2. Work out volumes for
various prisms.
3. Answer to contain
appropriate units and
working.
Volume of Solids
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Int 2
Definition : A prism is a solid shape with
uniform cross-section
Hexagonal Prism
Cylinder
(circular Prism)
Triangular Prism
Pentagonal Prism
Volume = Area of Cross section x length
Volume of Solids
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Int 2
Definition : A prism is a solid shape with
uniform cross-section
Q. Find the volume the triangular prism.
Triangular Prism
Volume = Area x length
3
= 20 x 10 = 200 cm
10cm
2
20cm
Volume of Solids
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Int 2
Definition : A prism is a solid shape with
uniform cross-section
Q. Find the volume the hexagonal prism.
Volume = Area x length
3
= 43.2 x 20 = 864 cm
20cm
2
43.2cm
Hexagonal Prism
Volume of Solids
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Int 2
Now try MIA Ex 3,4
Ch3 (page 24)
Starter
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Int 2
Q1.
Calculate the volume of the following cone.
1 2
Volume Cone = πr h
3
D = 6 cm
1
= π(3)2 ×10 h = 10 cm
3
= 30 cm 3
Q2.
h
r
My wages increased by 10% this year. My new wage
is £1200. What was my wage before the increase.
Volume of Solids
Prisms
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Int 2
Learning Intention
1. To calculate volumes for
composite shapes using
knowledge from previous
sections.
Success Criteria
1. To know what a composite
volume is.
2. Work out composite
volumes using previous
knowledge of basic prisms.
3. Answer to contain
appropriate units and
working.
Volume of a Solid
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Int 2
Composite volume
is simply volumes that are made up from basic volumes.
r
D
Volume =
h
4 3
πr
3
Volume = Area x length
r
Volume Cone =
1 2
πr h
3
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Int 2
Volume of a Solid
Composite volume
is simply volumes that are made up from basic volumes.
Q. Find the volume the composite shape.
Volume = Cylinder + half a sphere
Cylinder
V=πr h
2
=π(2)2 6
=24π m 3
Total 24 
½ sphere
1 4
V=  ( πr 3 )
2 3
1 4
=  ( π(2) 3 )
2 3
16
= π m3
3
16
88
=
π = 92.15m3
3
3
h = 6m
r
2m
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Int 2
Volume of a Solid
Composite Volumes
are simply volumes that are made up from basic volumes.
Q. This child’s toy is made from 2 identical cones.
Calculate the total volume.
Volume = 2 x cone
1 2
r = 10cm
πr h
3
1
h = 60cm
=  π  (10)2  30
3
Two cone
= 3141.5cm 3
= 2  3141.5 = 6283cm 3
One cone V =