Volume of a pyramid h Calculate the volume

Calculate the volume of the rectangular-based pyramid. 6 cm E D 4 cm C

Surface area of a pyramid h Surface area = sum of the areas of

Calculate the surface area of the rectangular-based pyramid. E First find the length of

E Area of rectangle ABCD = 4 × 5 = 20 cm 2 6.

7 cm Calculate the volume of the cone. 4 cm

Surface area of a cone The surface of a cone is made from a

Calculate a the curved surface area of the cone, b the total surface area

The straight edges of the sector are joined together to make a cone. Calculate

When you make a cut parallel to the base of a cone and remove

Calculate the volume of the frustum. All lengths are in cm. You must first

Volume and surface area of a sphere Volume of a sphere Surface area of

The sphere has radius 10 cm. Calculate a the volume of the sphere, b

The solid hemisphere has radius 6 cm. Calculate a the volume of the hemisphere,

The solid is made from a cylinder and a hemisphere. The cylinder has a

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Volume of a pyramid h

Calculate the volume of the rectangular-based pyramid. 6 cm E D 4 cm C A 5 cm B

Surface area of a pyramid h Surface area = sum of the areas of all the faces of the pyramid

Calculate the surface area of the rectangular-based pyramid. E First find the length of EX and EY. 6 cm Use Pythagoras on triangle EOX. D C X 4 cm O A Y 5 cm B Use Pythagoras on triangle EOY.

E Area of rectangle ABCD = 4 × 5 = 20 cm 2 6. 325 NET OF PYRAMID D 6. 5 A C 4 cm E 5 cm Area of triangle BCE = ½ × 4 × 6. 5 = 13 cm 2 B 6. 325 E Area of triangle CDE = ½ × 5 × 6. 325 = 15. 81 cm 2 6. 5 E Surface area = sum of areas of faces = 20 + 13 + 15. 81 = 77. 6 cm 2

Volume of a cone h r

7 cm Calculate the volume of the cone. 4 cm

Surface area of a cone The surface of a cone is made from a flat circular base and a curved surface. The curved surface is made from a sector of a circle. = FLAT BASE Curved surface area of a cone = , where Total surface area of a cone = + CURVED SURFACE is the slant height

Calculate a the curved surface area of the cone, b the total surface area of the cone. 12 cm a First calculate the slant height Curved surface area 5 cm b Total surface area using Pythagoras.

The straight edges of the sector are joined together to make a cone. Calculate a the curved surface area of the cone, b the radius of the base of the cone, c the height of the cone. 280 o cm 4 cm b Curved surface area 4 a Curved surface area = area of sector c Using Pythagoras 4 3. 11

When you make a cut parallel to the base of a cone and remove the top part, the part that is left is called a frustum. FRUSTUM Volume of frustum = volume of large cone – volume of smaller cone

Calculate the volume of the frustum. All lengths are in cm. You must first find the height of the smaller cone using similar triangles. 3 8 6 Volume of large cone Volume of small cone 3 8 6 Volume of frustum

Volume and surface area of a sphere Volume of a sphere Surface area of a sphere Volume and surface area of a hemisphere Volume of a hemisphere Curved surface area of a hemisphere A hemisphere is half a sphere.

The sphere has radius 10 cm. Calculate a the volume of the sphere, b the surface area of the sphere. a Volume b Surface area

The solid hemisphere has radius 6 cm. Calculate a the volume of the hemisphere, b the curved surface area of the hemisphere, c the total surface area of the hemisphere. a Volume b Curved surface area c Total surface area = area of base circle + curved surface area 6 cm

The solid is made from a cylinder and a hemisphere. The cylinder has a height of 8 cm and a radius of 3 cm. Calculate the volume of the solid. Volume of cylinder Volume of hemisphere Total volume