The figure shows a cylinder which is hollow in the middle and has a thickness of 10 cm. (Taking π=3.14\pi = 3.14.)

  1. (a)

    Find the area of the shaded face.

  2. (b)

    Randall dipped the entire cylinder into red paint. What is the surface area of the cylinder that is painted red?

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Worked solution

12(a)

1. Find the outer and inner radii of the shaded face

Outer radius R=60÷2=30 cmR = 60 \div 2 = 30\text{ cm}
Inner radius r=30−10=20 cmr = 30 - 10 = 20\text{ cm}

2. Calculate the area of the shaded face

Area=πR2−πr2\text{Area} = \pi R^2 - \pi r^2
Area=3.14×302−3.14×202\text{Area} = 3.14 \times 30^2 - 3.14 \times 20^2
Area=3.14×(900−400)\text{Area} = 3.14 \times (900 - 400)
Area=3.14×500=1570 cm2\text{Area} = 3.14 \times 500 = 1570\text{ cm}^2

Answer

1570 cm21570\text{ cm}^2

12(b)

1. Calculate the area of the two annular bases (top and bottom faces).

Area of one annular face =πR2−πr2=3.14×(302−202)=3.14×500=1570 cm2= \pi R^2 - \pi r^2 = 3.14 \times (30^2 - 20^2) = 3.14 \times 500 = 1570\text{ cm}^2
Area of two faces =2×1570=3140 cm2= 2 \times 1570 = 3140\text{ cm}^2

2. Calculate the outer and inner curved surface areas.

Outer curved surface area =2πRh=2×3.14×30×42=7912.8 cm2= 2\pi R h = 2 \times 3.14 \times 30 \times 42 = 7912.8\text{ cm}^2
Inner curved surface area =2πrh=2×3.14×20×42=5275.2 cm2= 2\pi r h = 2 \times 3.14 \times 20 \times 42 = 5275.2\text{ cm}^2

3. Find the total painted surface area.

Total surface area =3140+7912.8+5275.2=16328 cm2= 3140 + 7912.8 + 5275.2 = 16328\text{ cm}^2

Answer

16328 cm216328\text{ cm}^2

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