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Frustum

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by

Mr Mattock

on 24 June 2016

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Transcript of Frustum

Frustum
Starter
Based on this, write a definition for a frustum.
Frusta
Calculate the volume and surface area of this frustum
Activity
Complete the Frustum worksheet
L.O. - Calculate volumes and surface areas of frusta.
Starter
Based on this, write a definition for a frustum.
A frustum is the shape formed by slicing the top from a pyramid or cone using a
slice parallel to the base.
Volume
Calculate the volume of this frustum
Volume
Calculate the volume of this frustum
Height of small pyramid:
ratio of lengths = 9:15 = 3:5 = x:x+10
so 5x = 3x+30
2x = 30
x = 15
Volume of small pyramid:
x 9 x 15 = 405 cm
Volume of large pyramid:
x 15 x 25 = 1875 cm
Volume of frustum:
1875 - 405 = 1470 cm
1
3
1
3
2
2
3
3
3
Surface Area
Surface Area
y:
y = 10 + 3 = 109.
y = 109
2
2
2
Area of side trapezia:
(15 + 9) x 109
= 12 109.
Surface area: (4 trapezia, plus top and bottom squares)
15 + 9 + 4 x 12 109 = 306 + 48 109 cm
2
1
2
2
2
Find the surface area of this frustum
Find the surface area of this frustum
Activity
Complete the Frustum worksheet
1) i) V = 1265, SA = 393 (ii) V = 508, SA = 244 (iii) V = 490, SA = 295

2) V = 50 , SA = 92

3) a) h b) r h c) (2r) (2h) = r h d) r h
2
3
1
3
2
2
2
8
3
1
3
2
8
3
Activity
Answers

Activities
Key
Examples

Worked
Example

Surface
Area

Volume
Worked
Example
Full transcript