2. Whiteboardmaths.com © 2004 All rights reserved 5 7 2 1

3. Composite Solids

4. Area Composite Solids An aeronautical engineer designs a small component part made of copper, that is to be used in the manufacturer of an aircraft. The part consists of a cone that sits on top of a cylinder as shown in the diagram below. Find the surface area of the part excluding the base. (Leave your answer in terms of  ). Surface area of cone =  rl 10 cm 7 cm 6 cm =  x 3.5 x 10 = 35  cm 2 Surface area of cylinder = 2  rh = 2 x  x 3.5 x 6 = 42  cm 2 Total surface area = 35  + 42  = 77  cm 2 Example Question 1

5. Composite Solids The diagram below shows a design for a water tank. The water tank consists of a cylinder capped with a hemi-spherical dome. Find the surface area of the water tank, excluding the base. (Leave your answer in terms of  ). Surface area of hemi-sphere = 2  r 2 = 2 x  x 3 2 = 18  m 2 Surface area of cylinder = 2  rh = 2 x  x 3 x 5 = 30  m 2 Total surface area = 18  + 30  = 48  m 2 6 m 5m Example Question 2

6. Composite Solids A fuel pod consists of cylinder with a hemi-spherical base and a conical top as shown in the diagram. Calculate the surface area of the pod. (answer to 2 sig fig) Surface area of hemi-sphere = 2  r 2 = 2 x  x 5 2 = 50  cm 2 Surface area of cylinder = 2  rh = 2 x  x 5 x 40 = 400  cm 2 Surface area of cone =  rl 10 cm 40 cm 12 cm =  x 5 x 12 = 60  cm 2 Total surface area = 60  + 400  + 50  = 510  cm 2 = 1600 cm 2 Example Question 3

7. Composite Solids An aeronautical engineer designs a small component part made of copper, that is to be used in the manufacturer of an aircraft. The part consists of a cone that sits on top of a cylinder as shown in the diagram below. Find the surface area of the part excluding the base. (Leave your answer in terms of  ). Surface area of cone =  rl 11 cm 8 cm 7 cm =  x 4 x 11 = 44  cm 2 Surface area of cylinder = 2  rh = 2 x  x 4 x 7 = 56  cm 2 Total surface area = 44  + 56  = 100  cm 2 Question 1

8. Composite Solids The diagram below shows a design for a water tank. The water tank consists of a cylinder capped with a hemi-spherical dome. Find the surface area of the water tank, excluding the base. (Leave your answer in terms of  ). Surface area of hemi-sphere = 2  r 2 = 2 x  x 4 2 = 32  m 2 Surface area of cylinder = 2  rh = 2 x  x 4 x 6 = 48  m 2 Total surface area = 32  + 48  = 80  m 2 8 m 6m Question 2

9. Composite Solids A fuel pod consists of cylinder with a hemi-spherical base and a conical top as shown in the diagram. Calculate the surface area of the pod. (answer to 3 sig fig) Surface area of hemi-sphere = 2  r 2 = 2 x  x 4 2 = 32  cm 2 Surface area of cylinder = 2  rh = 2 x  x 4 x 30 = 240  cm 2 Surface area of cone =  rl 8 cm 30 cm 10 cm =  x 4 x 10 = 40  cm 2 Total surface area = 40  + 240  + 32  = 312  cm 2 = 980 cm 2 Question 3

10. Vol/Cap Composite Solids An aeronautical engineer designs a small component part made of copper, that is to be used in the manufacturer of an aircraft. The part consists of a cone that sits on top of a cylinder as shown in the diagram below. Find the volume of the part. (Leave your answer in terms of  ). Volume of cone = 1/3  r 2 h 8 cm 6 cm = 1/3 x  x 4 2 x 9 = 48  cm 3 Volume of cylinder =  r 2 h =  x 4 2 x 6 = 96  cm 3 Total volume = 48  + 96  = 144  cm 3 Example Question 1 9 cm

11. Composite Solids The shape below is composed of a solid metal cylinder capped with a solid metal hemi-sphere as shown. Find the volume of the shape. (to 3 sig fig) Volume of hemi-sphere = 2/3  r 3 = 2/3 x  x 3 3 = 18  m 3 Volume of cylinder =  r 2 h =  x 3 2 x 4 = 36  m 3 Total volume = 18  + 36  = 54  m 3 6 m 4m Example Question 2 = 170 m 3

12. Composite Solids The diagram below shows a design for a water tank. The water tank consists of a cylinder capped with a hemi-spherical dome. Find the capacity of the water tank. (Give your answer in litres to 2 sig fig). Capacity of hemi-sphere = 2/3  r 3 = 2/3 x  x 3 3 = 18  m 3 Capacity of cylinder =  r 2 h =  x 3 2 x 5 = 45  m 3 Total capacity = 18  + 45  = 63  m 3 6 m 5m Example Question 3 = 63 000 000  cm 3 = 63 000  litres = 200 000 litres (2 sig fig) 100 cm 1 000 000 cm 3 10 cm 1 000 cm 3 1 litre

13. Composite Solids A solid shape is composed of a cylinder with a hemi-spherical base and a conical top as shown in the diagram. Calculate the volume of the shape. (answer to 2 sig fig) Volume of hemi-sphere = 2/3  r 3 = 2/3 x  x 6 3 = 144  cm 3 Volume of cylinder =  r 2 h =  x 6 2 x 40 = 1440  cm 3 Volume of cone = 1/3 x  r 2 h 12 cm 40 cm = 1/3 x  x 6 2 x 14 = 168  cm 3 Total volume = 168  + 1440  + 144  = 1752  cm 3 = 5500 cm 3 Example Question 4 14 cm

14. Composite Solids An aeronautical engineer designs a small component part made of copper, that is to be used in the manufacturer of an aircraft. The part consists of a cone that sits on top of a cylinder as shown in the diagram below. Find the volume of the part. (Leave your answer in terms of  ). Volume of cone = 1/3  r 2 h 10 cm 6 cm = 1/3 x  x 5 2 x 12 = 100  cm 3 Volume of cylinder =  r 2 h =  x 5 2 x 6 = 150  cm 3 Total volume = 100  + 150  = 250  cm 3 Question 1 12 cm

15. Composite Solids The shape below is composed of a solid metal cylinder capped with a solid metal hemi-sphere as shown. Find the volume of the shape. (to 2 sig fig) Volume of hemi-sphere = 2/3  r 3 = 2/3 x  x 9 3 = 486  cm 3 Volume of cylinder =  r 2 h =  x 9 2 x 10 = 810  m 3 Total volume = 486  + 810  = 1296  cm 3 18 cm 10 cm Question 2 = 4100 cm 3

16. Composite Solids The diagram below shows a design for a water tank. The water tank consists of a cylinder capped with a hemi-spherical dome. Find the capacity of the water tank. (Give your answer in litres to 3 sig fig). Capacity of hemi-sphere = 2/3  r 3 = 2/3 x  x 6 3 = 144  m 3 Capacity of cylinder =  r 2 h =  x 6 2 x 10 = 360  m 3 Total capacity = 144  + 360  = 504  m 3 12 m 10m Question 3 = 504 000 000  cm 3 = 504 000  litres = 1 580 000 litres (3 sig fig) 100 cm 1 000 000 cm 3 10 cm 1 000 cm 3 1 litre

17. Composite Solids A solid shape is composed of a cylinder with a hemi-spherical base and a conical top as shown in the diagram. Calculate the volume of the shape. (answer to 2 sig fig) Volume of hemi-sphere = 2/3  r 3 = 2/3 x  x 3 3 = 18  cm 3 Volume of cylinder =  r 2 h =  x 3 2 x 20 = 180  cm 3 Volume of cone = 1/3 x  r 2 h 6 cm 20 cm = 1/3 x  x 3 2 x 9 = 27  cm 3 Total volume = 27  + 180  + 18  = 225  cm 3 = 710 cm 3 Question 4 9 cm

18. Worksheets Surface Area Example Questions

19. Surface Area Questions

20. Volume/Capacity Example Questions

21. Volume/Capacity Questions