1. Key words Formula Volume Surface area Perpendicular Height
LO: Calculate the volume and surface area of a Sphere and Cone (Grade A)
Key words
Formula
Volume
Surface area
Perpendicular Height
Slant Height
Frustum
Vertex
Midpoint
Cone
Sphere

2. LO: Calculate the volume and surface area of a Sphere and Cone (Grade A)
Example 1 Cone
Curved surface area of a cone = TT r l
Total surface area of a cone = TT r l + TT r²
Volume = TT r²h 3
Curved surface area = TT x 5 x 12 = =
Base area = TT r²
= TT x 5²
= 78.54
Total surface area = = cm²
Volume = TT x 5² x 10 = = cm³
R = 5
H = 10
L = 12

3. V = 14241.89cm³ V = 20.94cm³ SA = 3480.89cm² SA = 56.54cm²
LO: Calculate the volume and surface area of a Sphere and Cone (Grade A)
V = cm³
SA = cm²
V = 20.94cm³
SA = 56.54cm²
V = cm³
SA = cm²
V = cm³
SA = cm²
8cm

4. Calculate the volume and surface area of the sphere below:
LO: Calculate the volume and surface area of a Sphere and Cone (Grade A)
Calculate the volume and surface area of the sphere below:
r = 4
Volume of a sphere =
Surface area of a sphere =
Surface area of a sphere =
Volume of a sphere =
Volume of a sphere =
Surface area of a sphere =
Volume of a sphere =
Surface area of a sphere =

5. Find the volume and surface area of these spheres
LO: Calculate the volume and surface area of a Sphere and Cone (Grade A)
Find the volume and surface area of these spheres
V = 1437cm³
SA = cm²
V = 57906cm³
SA = cm²
V = cm³
SA = cm²
51.2cm
V = mm³
SA = mm²
V = cm³
SA = cm²
V = cm³
SA = cm²
R = 135 mm

6. Finding the radius given the volume of a sphere
Find the radius of a sphere of volume 240 𝑐𝑚 3
Volume = 4 3 π 𝑟 3
240 = π 𝑟 3
240 4π 3 = 𝑟 3
57.29 = 𝑟 r = 3.86cm

7. Finding the radius given the volume of the cone
Find the radius of a cone of volume 85 𝑐𝑚 3 and height 5cm.
V = 1 3 π 𝑟 2 h
85 = π 𝑟 2 x 5
π 𝑥 5 = 𝑟 2
16.23 = 𝑟 2 r = 4.03cm

8. This means that the diameter of the ball is the length of the box.
Diameter = 25cm. Therefore radius = 12.5cm
a) SA = 4π 𝑟 2
= 4 x π x = 𝑐𝑚 2
b) V = 4 3 π 𝑟 3
V = π 𝑥 = 𝑐𝑚 3

9. V of a sphere = π 𝑟 3
V = 𝑥 π 𝑥 5 3 = 𝑐𝑚 3
Since the cone and sphere have the same volume…
V of cone = π 𝑟 2 ℎ
= π 8 2 ℎ
𝑥 π 𝑥 = h
h = 7.81cm

10. Past exam Questions Volume of a cylinder: πr²h TT x 5² x 30
LO: Calculate the volume and surface area of a Sphere and Cone (Grade A)
Past exam Questions
Volume of a cylinder: πr²h
TT x 5² x 30
TT x 5² x 30 = 𝑐𝑚 3
4/3 x π x 5³ = 𝑐𝑚 3
Vol of 3 spheres = X 3 =
Volume remaining = – = 785.4cm³

11. LO: Calculate the volume and surface area of a Sphere and Cone (Grade A)
Past exam Questions
A marble paperweight consists of a cuboid and a hemisphere as shown in the diagram. The hemisphere has a radius of 4 cm. Calculate the volume of the paperweight
V of sphere = 4 3 π 𝑟 3
= 4 3 π 𝑥 = 𝑐𝑚 3
V of hemisphere = ÷ 2 = 𝑐𝑚 3
V of cuboid = Area x height
= 10 x 10 x 5 = 500 𝑐𝑚 3
Total volume = = 𝑐𝑚 3

12. LO: Calculate the volume and surface area of a Sphere and Cone (Grade A)
Past exam Questions
A hemispherical bowl of radius 6 cm has the same volume as a cone of perpendicular height 27 cm. Not drawn accurately
          Calculate the base radius, r, of the cone.

13. LO: Calculate the volume and surface area of a Sphere and Cone (Grade A)
Past exam Questions
A cone has base radius 6 cm and height h = 9 cm. A smaller cone of base radius 2 cm and height 3 cm is cut from the top. The remaining frustum has dimensions as shown.
Calculate the volume of the frustum
 Volume of the frustum =
Vol of the large cone – Vol of small cone
1 3 𝑥 π 𝑥 6 2 𝑥 𝑥 π 𝑥 2 2 𝑥 3 = 𝑐𝑚 3

14. Past exam Questions Calculate the volume and surface area:
LO: Calculate the volume and surface area of a Sphere and Cone (Grade A)
Past exam Questions .
10cm
16cm
Calculate the volume and surface area:

15. LO: Calculate the volume and surface area of a Sphere and Cone (Grade A)

16. A cylinder of radius 5cm and height 6cm is melted and recast into a cone of radius 3cm. What is the height of the cone?
V=π 𝑟 2 ℎ
V = π x x 6
V = 𝑐𝑚 3
V = 1 3 π 𝑟 2 h
471.2= 1 3 π 𝑟 2 ℎ

17. A cone of radius 6cm and height 4cm is melted and recast into spheres of radius 1cm. How many spheres are made?
Volume of cone = 1 3 π 𝑟 2 ℎ
V = 1 3 π 6 2 𝑥 4 = 𝑐𝑚 3
Volume of sphere = 4 3 π 𝑟 3
= 4 3 π = 4.19 𝑐𝑚 3
Number of spheres = ÷ 4.19 = 36 spheres
( if the answer is not a whole number, give the answer as a whole number, rounded down)