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Calculate the total surface area of a cylinder with radius 7 cm and height 10 cm, using pi = 22/7.

Mathematics

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Here's the solution for question 11:

Given:
Radius r=7r = 7 cm
Height h=10h = 10 cm
Use π=227\pi = \frac{22}{7}

  1. Find the area of the two circular faces.

    The area of one circular face is given by the formula Acircle=πr2A_{circle} = \pi r^2.
    The area of two circular faces is 2×πr22 \times \pi r^2.

    Atwo_circles=2×227×(7 cm)2A_{two\_circles} = 2 \times \frac{22}{7} \times (7 \text{ cm})^2 Atwo_circles=2×227×49 cm2A_{two\_circles} = 2 \times \frac{22}{7} \times 49 \text{ cm}^2 Atwo_circles=2×22×7 cm2A_{two\_circles} = 2 \times 22 \times 7 \text{ cm}^2 Atwo_circles=308 cm2A_{two\_circles} = 308 \text{ cm}^2

    The area of the two circular faces is 308 cm2\boxed{\text{308 cm}^2}.

  2. Find the area of the curved surface.

    The area of the curved surface of a cylinder is given by the formula Acurved=2πrhA_{curved} = 2 \pi r h.

    Acurved=2×227×7 cm×10 cmA_{curved} = 2 \times \frac{22}{7} \times 7 \text{ cm} \times 10 \text{ cm} Acurved=2×22×10 cm2A_{curved} = 2 \times 22 \times 10 \text{ cm}^2 Acurved=440 cm2A_{curved} = 440 \text{ cm}^2

    The area of the curved surface is 440 cm2\boxed{\text{440 cm}^2}.

  3. Find the total surface area of the can.

    The total surface area is the sum of the area of the two circular faces and the area of the curved surface.

    Atotal=Atwo_circles+AcurvedA_{total} = A_{two\_circles} + A_{curved} Atotal=308 cm2+440 cm2A_{total} = 308 \text{ cm}^2 + 440 \text{ cm}^2 Atotal=748 cm2A_{total} = 748 \text{ cm}^2

    The total surface area of the can is 748 cm2\boxed{\text{748 cm}^2}.

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