Volume of a pyramid h Calculate the volume

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Volume of a pyramid h

Volume of a pyramid h

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

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

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

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.

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

Volume of a cone h r

7 cm Calculate the volume of the cone. 4 cm

7 cm Calculate the volume of the cone. 4 cm

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

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

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

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

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

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

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 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,

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

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