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A cylindrical can has a diameter of 55 mm and a height of 16 cm. Calculate its radius and total surface area (rounded to the nearest cm²).

Mathematics

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3 parts
3.1

2.75 cm\text{2.75 cm}

3.2

358 cm2\text{358 cm}^2

3.3

125.3 cm2\text{125.3 cm}^2

Step-by-step solution

8 steps

Here are the solutions to the questions:

Part 3.1· 2 steps

Determine the radius of the can, in cm.

  1. Identify the given diameter and convert it to centimeters.

    The diameter of the can is given as 55 mm55 \text{ mm}.
    Since 1 cm=10 mm1 \text{ cm} = 10 \text{ mm}, we convert the diameter to centimeters:

    Diameter=55 mm×1 cm10 mm=5.5 cm\text{Diameter} = 55 \text{ mm} \times \frac{1 \text{ cm}}{10 \text{ mm}} = 5.5 \text{ cm}

  2. Calculate the radius using the diameter.

    The radius is half of the diameter.

    Radius=Diameter2=5.5 cm2=2.75 cm\text{Radius} = \frac{\text{Diameter}}{2} = \frac{5.5 \text{ cm}}{2} = 2.75 \text{ cm}

    The radius of the can is 2.75 cm\boxed{\text{2.75 cm}}.

Part 3.2

358 cm2\text{358 cm}^2

Calculate the total surface area of the can, rounded to the nearest cm², if the radius of the can is rounded to 3 cm.

  1. Identify the given values for radius, height, and π\pi.

    For this calculation, the radius is given as 3 cm3 \text{ cm}.
    The height of the can is 16 cm16 \text{ cm}.
    The value of π\pi is given as 3.142.

  2. Use the formula for the surface area of a cylinder.

    The formula for the surface area of a cylinder is:

    Surface area=2×π×radius2+2×π×radius×height\text{Surface area} = 2 \times \pi \times \text{radius}^2 + 2 \times \pi \times \text{radius} \times \text{height}

  3. Substitute the values into the formula and calculate.

    Surface area=(2×3.142×(3 cm)2)+(2×3.142×3 cm×16 cm)\text{Surface area} = (2 \times 3.142 \times (3 \text{ cm})^2) + (2 \times 3.142 \times 3 \text{ cm} \times 16 \text{ cm}) Surface area=(2×3.142×9 cm2)+(2×3.142×48 cm2)\text{Surface area} = (2 \times 3.142 \times 9 \text{ cm}^2) + (2 \times 3.142 \times 48 \text{ cm}^2) Surface area=56.556 cm2+301.632 cm2\text{Surface area} = 56.556 \text{ cm}^2 + 301.632 \text{ cm}^2 Surface area=358.188 cm2\text{Surface area} = 358.188 \text{ cm}^2

  4. Round the surface area to the nearest cm².

    Surface area≈358 cm2\text{Surface area} \approx 358 \text{ cm}^2

    The total surface area of the can, rounded to the nearest cm², is 358 cm2\boxed{\text{358 cm}^2}.

Part 3.3

125.3 cm2\text{125.3 cm}^2

The area of the label of the can covers 35% of the total surface area of the can. Calculate the total area covered by the label of the can.

  1. Identify the total surface area from the previous calculation and the percentage covered by the label.

    Total surface area = 358 cm2358 \text{ cm}^2 (from question 3.2).
    Percentage covered by the label = 35%35\%.

  2. Calculate the area covered by the label.

    Label area=35% of 358 cm2\text{Label area} = 35\% \text{ of } 358 \text{ cm}^2 Label area=0.35×358 cm2\text{Label area} = 0.35 \times 358 \text{ cm}^2 Label area=125.3 cm2\text{Label area} = 125.3 \text{ cm}^2

    The total area covered by the label of the can is 125.3 cm2\boxed{\text{125.3 cm}^2}.

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