1. Volume of a pyramid/Sphere
Thursday, 23 May 2019

2. Volume of a pyramid 𝑉𝑜𝑙𝑢𝑚𝑒= 1 3 ×𝐵𝑎𝑠𝑒 𝐴𝑟𝑒𝑎×ℎ𝑒𝑖𝑔ℎ𝑡 Square based pyramid
Tetrahedron
cone
𝑉𝑜𝑙𝑢𝑚𝑒= 1 3 ×𝐵𝑎𝑠𝑒 𝐴𝑟𝑒𝑎×ℎ𝑒𝑖𝑔ℎ𝑡

3. Example Find the volume for each of the following pyramids (i)
7×5
=35
Base Area =
7cm
5cm
4cm
1 3 ×35×4
Volume =
=46.67
cm3

4. (ii)
3cm
6cm
3×3 =9
Base Area =
1 3 ×9×6
Volume =
=18
cm3

5. (iii) 8cm 5cm 𝜋× 2.5 2 =19.63 1 3 ×19.63×8 =52.36 Base Area = Volume =

6. (iv) 6cm 5cm 𝜋× 5 2 =78.54 1 3 ×78.54×6 =157.08 Base Area = Volume =

7. Example
Which has the greatest volume?
3.2cm
7cm
3.2cm
7cm
𝜋× 3.2 2
=32.17
Base Area =
3.2×3.2
=10.24
Base Area =
1 3 ×32.17×7
1 3 ×10.24×7
Volume =
Volume =
=75.06
cm3
=23.89
cm3
Cone has the greatest volume

8. Example
A teal plug is machined into the shape of a truncated cone, with end radii of 1.5cm and 2.4cm.
Find the volume of the plug
𝜋× 1.5 2
=7.07
Base Area =
2.4cm
1.5
3.5cm
4.5cm
1 3 ×7.07×4.5
Volume =
=10.60
𝜋× 2.4 2
=18.10
Base Area =
1 3 ×18.10×8
Volume =
Volume of plug =
37.65
cm3
=48.25

9. Volume of a sphere
𝑉𝑜𝑙𝑢𝑚𝑒= 4 3 𝜋 𝑟 3
radius

10. Find the volume of the following spheres (i)
Example
Find the volume of the following spheres
(i)
3.2cm
𝑉𝑜𝑙𝑢𝑚𝑒= 4 3 𝜋 𝑟 3
= 4 3 𝜋× 3.2 3
=137.26
cm3

11. (ii)
𝑉𝑜𝑙𝑢𝑚𝑒= 4 3 𝜋 𝑟 3
= 4 3 𝜋× 23 3 =
cm3
=0.051 m3
46cm

12. Example
The diagram below is of a bowl which consists of a hemi-sphere of diameter 20cm with a smaller hemi-sphere, of radius 9cm, cut out. Find the volume of the bowl.

13. 𝑉𝑜𝑙𝑢𝑚𝑒= 2 3 𝜋 𝑟 3 = 4 3 𝜋× 10 3 = 2 3 𝜋× 9 3 𝑉𝑜𝑙𝑢𝑚𝑒 =2094.40 =1526.81
𝑉𝑜𝑙𝑢𝑚𝑒= 2 3 𝜋 𝑟 3
= 4 3 𝜋× 10 3
= 2 3 𝜋× 9 3
𝑉𝑜𝑙𝑢𝑚𝑒 = =
𝑉𝑜𝑙𝑢𝑚𝑒= −
=567.58
cm3