2. Volume of a pyramid h

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

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

5. 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

6. 6.5 6.325 5 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 × 6.325 = 15.81 cm 2 = 20 + 13 + 13 + 15.81 + 15.81 = 77.6 cm 2 NET OF PYRAMID

7. Volume of a cone h r

8. Calculate the volume of the cone. 7 cm 4 cm

9. 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 =

10. 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

11. 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 3.11 4

12. 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

13. Calculate the volume of the frustum. All lengths are in cm. 3 6 8 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

14. 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.

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

16. 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

17. 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