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

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 = 188.4955 = 188.50 Base area = TT r² = TT x 5² = 78.54 Total surface area = 188.50 + 78.54 = 267.01cm² Volume = TT x 5² x 10 = 785.3981634 = 261.80 cm³ 3 3 R = 5 H = 10 L = 12

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 = 14241.89cm³ SA = 3480.89cm² V = 20.94cm³ SA = 56.54cm² V = 314.16cm³ SA = 282.74cm² V = 167.55cm³ SA = 201.07cm² 8cm

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 =

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 = 615.75cm² V = 57906cm³ SA = 7238.23cm² V = 1047.39cm³ SA = 498.76cm² 51.2cm V =10305994.70 mm³ SA = 229022.10mm² V = 70276.24cm³ SA = 8235.50cm² V = 24429.02cm³ SA = 4071.56 cm² R = 135 mm

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 = 4 3 π 𝑟 3 240 4π 3 = 𝑟 3 57.29 = 𝑟 3 r = 3.86cm

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 = 1 3 π 𝑟 2 x 5 85 1 3 π 𝑥 5 = 𝑟 2 16.23 = 𝑟 2 r = 4.03cm

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 12.5 2 = 1963.5 𝑐𝑚 2 b) V = 4 3 π 𝑟 3 V = 4 3 π 𝑥 12.5 3 = 8181.2 𝑐𝑚 3

V of a sphere = 4 3 π 𝑟 3 V = 4 3 𝑥 π 𝑥 5 3 = 523.6 𝑐𝑚 3 Since the cone and sphere have the same volume… V of cone = 1 3 π 𝑟 2 ℎ 523.6 = 1 3 π 8 2 ℎ 523.6 1 3 𝑥 π 𝑥 8 2 = h h = 7.81cm

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 = 2356.19449 𝑐𝑚 3 4/3 x π x 5³ = 523.5987756 𝑐𝑚 3 Vol of 3 spheres = 523.6 X 3 = 1570.80 Volume remaining = 2356.20 – 1570.80 = 785.4cm³

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 4 3 = 268.08 𝑐𝑚 3 V of hemisphere = 268.08 ÷ 2 = 134.04 𝑐𝑚 3 V of cuboid = Area x height = 10 x 10 x 5 = 500 𝑐𝑚 3 Total volume = 134.04 + 500 = 634.04 𝑐𝑚 3

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.

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 9 - 1 3 𝑥 π 𝑥 2 2 𝑥 3 = 326. 𝑐𝑚 3

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:

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

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 5 2 x 6 V = 471.2 𝑐𝑚 3 V = 1 3 π 𝑟 2 h 471.2= 1 3 π 𝑟 2 ℎ

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 = 150.8 𝑐𝑚 3 Volume of sphere = 4 3 π 𝑟 3 = 4 3 π 1 3 = 4.19 𝑐𝑚 3 Number of spheres = 150.8 ÷ 4.19 = 36 spheres ( if the answer is not a whole number, give the answer as a whole number, rounded down)