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Composite Solids

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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Worksheets Surface Area Example Questions

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Surface Area Questions

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Volume/Capacity Example Questions

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Volume/Capacity Questions

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Volume of Composite Solids

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