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A 215-litre drum has a radius of 26 cm. Calculate its height and surface area.

Mathematics

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4.3.1)

  1. Use the given conversion factor.

    Given that 1 ℓ=1000 cm31\, \ell = 1000\, \text{cm}^3.

  2. Convert the volume from litres to cubic centimetres.

    215 ℓ×1000 cm31 ℓ=215000 cm3215\, \ell \times \frac{1000\, \text{cm}^3}{1\, \ell} = 215000\, \text{cm}^3

    The volume is 215000 cm3^3.

    215000 cm3\boxed{215000\, \text{cm}^3}

    4.3.2)

  3. State the formula for the volume of a cylinder and the given values.

    The formula for the volume of a cylinder is V=πr2hV = \pi r^2 h.
    From 4.3.1, V=215000 cm3V = 215000\, \text{cm}^3.
    The radius is r=26 cmr = 26\, \text{cm}.
    Use π=3.14\pi = 3.14.

  4. Substitute the values into the volume formula.

    215000 cm3=(3.14)×(26 cm)2×h215000\, \text{cm}^3 = (3.14) \times (26\, \text{cm})^2 \times h

  5. Calculate r2r^2.

    215000 cm3=(3.14)×(676 cm2)×h215000\, \text{cm}^3 = (3.14) \times (676\, \text{cm}^2) \times h

  6. Multiply π\pi by r2r^2.

    215000 cm3=2122.64 cm2×h215000\, \text{cm}^3 = 2122.64\, \text{cm}^2 \times h

  7. Solve for hh.

    h=215000 cm32122.64 cm2h = \frac{215000\, \text{cm}^3}{2122.64\, \text{cm}^2} h≈101.288 cmh \approx 101.288\, \text{cm}

  8. Round the height to the nearest whole number as requested (approximately 101 cm).

    h≈101 cmh \approx 101\, \text{cm}

    The height of the drum is approximately 101 cm.

    101 cm\boxed{101\, \text{cm}}

    4.3.3)

  9. State the formula for the surface area of a cylinder and the given values.

    The formula for the surface area is A=2πr2+2πrhA = 2\pi r^2 + 2\pi rh.
    The radius is r=26 cmr = 26\, \text{cm}.
    The height is h=101 cmh = 101\, \text{cm} (from 4.3.2).
    Use π=3.14\pi = 3.14.

  10. Substitute the values into the surface area formula.

    A=2×(3.14)×(26 cm)2+2×(3.14)×(26 cm)×(101 cm)A = 2 \times (3.14) \times (26\, \text{cm})^2 + 2 \times (3.14) \times (26\, \text{cm}) \times (101\, \text{cm})

  11. Calculate the terms.

    A=2×3.14×676 cm2+2×3.14×26 cm×101 cmA = 2 \times 3.14 \times 676\, \text{cm}^2 + 2 \times 3.14 \times 26\, \text{cm} \times 101\, \text{cm} A=4245.28 cm2+16479.28 cm2A = 4245.28\, \text{cm}^2 + 16479.28\, \text{cm}^2

  12. Add the terms to find the total surface area.

    A=20724.56 cm2A = 20724.56\, \text{cm}^2

    The surface area of the oil drum is 20724.56 cm2^2.

    20724.56 cm2\boxed{20724.56\, \text{cm}^2}

    4.3.4)

  13. State the relationship between diameter and radius.

    The diameter DD is twice the radius rr.

    D=2rD = 2r

  14. Substitute the given radius.

    The radius is r=26 cmr = 26\, \text{cm}.

    D=2×26 cmD = 2 \times 26\, \text{cm} D=52 cmD = 52\, \text{cm}

    The diameter of the tank is 52 cm.

    52 cm\boxed{52\, \text{cm}}
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