Volume of a pyramid h

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

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

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

cm 4 cm A B CD E E EE Surface area = sum of areas of faces Area of rectangle ABCD =4 × 5 = 20 cm 2 Area of triangle BCE =½ × 4 × 6.5 = 13 cm 2 Area of triangle CDE =½ × 5 × = cm 2 = = 77.6 cm 2 NET OF PYRAMID

Volume of a cone h r

Calculate the volume of the cone. 7 cm 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 = Curved surface area of a cone =, where is the slant height Total surface area of a cone =

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

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

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. Volume of large coneVolume of small cone Volume of frustum 3 6 8

Volume and surface area of a sphere Volume of a sphere Volume of a sphere Surface area of a sphere Volume and surface area of a hemisphere Volume 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. Calculatea 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. 6 cm a Volume b Curved surface area c Total surface area = area of base circle + curved surface area

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