Learning Objective: Find the volume and surface area of pyramids, cones and spheres.

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