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Convert the volume of 215 ℓ to cubic centimetres. Use your answer to show that the height of the drum is approximately 101 cm. Sfiso wanted to paint the oil drum. Determine the surface area of the oil

Mathematics

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4.3.1 Convert the volume of 215 ℓ\ell to cubic centimetres.

  1. Use the given conversion factor 1ℓ=1000 cm31 \ell = 1000 \text{ cm}^3.

    215ℓ×1000 cm31ℓ=215000 cm3215 \ell \times \frac{1000 \text{ cm}^3}{1 \ell} = 215000 \text{ cm}^3

    The volume is 215000 cm3\boxed{\text{215000 cm}^3}.

    4.3.2 Use your answer in 4.3.1 to show that the height of the drum is approximately 101 cm.

  2. Identify the given values

    Volume (VV) from 4.3.1 is 215000 cm3215000 \text{ cm}^3, radius (rr) is 26 cm26 \text{ cm}, and π=3.14\pi = 3.14.

  3. Use the formula for the volume of a cylinder, V=πr2hV = \pi r^2 h, and rearrange to solve for hh.

    h=Vπr2h = \frac{V}{\pi r^2}
  4. Substitute the values into the formula.

    h=215000 cm33.14×(26 cm)2h = \frac{215000 \text{ cm}^3}{3.14 \times (26 \text{ cm})^2} h=215000 cm33.14×676 cm2h = \frac{215000 \text{ cm}^3}{3.14 \times 676 \text{ cm}^2} h=215000 cm32122.24 cm2h = \frac{215000 \text{ cm}^3}{2122.24 \text{ cm}^2} h≈101.31 cmh \approx 101.31 \text{ cm}

    The height of the drum is approximately 101 cm\boxed{\text{101 cm}}.

    4.3.3 Sfiso wanted to paint the oil drum. Determine the surface area of the oil drum if the entire oil drum must be painted. Write your answer with correct units of measurement.

  5. Identify the given values

    radius (rr) is 26 cm26 \text{ cm}, height (hh) is 101 cm101 \text{ cm} (from 4.3.2), and π=3.14\pi = 3.14.

  6. Use the formula for the surface area of a cylinder, SA=2πr2+2πrhSA = 2\pi r^2 + 2\pi rh.

    SA=(2×3.14×(26 cm)2)+(2×3.14×26 cm×101 cm)SA = (2 \times 3.14 \times (26 \text{ cm})^2) + (2 \times 3.14 \times 26 \text{ cm} \times 101 \text{ cm}) SA=(2×3.14×676 cm2)+(2×3.14×2626 cm2)SA = (2 \times 3.14 \times 676 \text{ cm}^2) + (2 \times 3.14 \times 2626 \text{ cm}^2) SA=(4245.28 cm2)+(16493.44 cm2)SA = (4245.28 \text{ cm}^2) + (16493.44 \text{ cm}^2) SA=20738.72 cm2SA = 20738.72 \text{ cm}^2

    The surface area of the oil drum is 20738.72 cm2\boxed{\text{20738.72 cm}^2}.

    4.3.4 Calculate the diameter of the tank.

  7. Identify the given radius (rr) as 26 cm26 \text{ cm}.

  8. Use the formula for diameter, D=2rD = 2r.

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

    The diameter of the tank is 52 cm\boxed{\text{52 cm}}.

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