Learning Objective: Find the volume and surface area of pyramids, cones and spheres.
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Learning Objective:
1)Find the volume and surface area of pyramids, cones and spheres.
2) Find the volume of a frustum
Most of the questions on this subject are towards the end of the Higher paper... So they are generally harder
Calculate the Volume and Surface Area of the Frustum
Knowing the volume and surface area of the Frustum, how would I approach this problem?
Calculate the Volume and Surface Area of the Frustum
Start with Volume – it is easier!!!
2
2
2
3
13
1 6 8 963
1 3 4 123
96 12 84 cm
big
small
Frustum
V r h
V
V
V
Calculate the Volume and Surface Area of the Frustum
Now Surface Area
2
6 10 60
3 5 15
60 15 45 cm
big
small
Frustum
SA rlSA
SA
SA
2
2
9
36
Top r
Bottom r
2
2
45 36 9 90 cm
283
Total
Total cm
3sphere
: d=6, r=34V 363
1 182Hemisphere sphere
Hemisphere
r
V V
2
:12 3 9
9 9 81
18 81 99
cylinder
total hemisphere cylinder
Cylinderh
V r h
V V V
V
2
2
1 99 49.52
18
49.5 18 31.5
31.5 31.5 3.59 9
3.5 3 (from hemisphere) = 6.5
hemisphere
left
V
V
V
V r hVhr
d
3
3
1 42 3
2 26 2163 3144
hemisphereV r
V
V
2
2
2
13
1 2739
coneV r h
V r
V r
2
2
2
Equate both Volumes
9 r 144144
9144
94
r
r
r
Learning Objective:
1)Find the volume and surface area of pyramids, cones and spheres.
2) Find the volume of a frustum
For the remainder of this lesson and for this week’s homework, you will have an GCSE paper with questions related to area and volume and circle theorems.
Most of the answers are incorrect.Your task is to find the error and correct the paper
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