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Thabiso places 6 cylinders on the three cuboids as shown. The first row of cylinders leaves an equal distance of 4.5 cm on either side. Find the diameter of each cylinder.

Mathematics

ScanSolve AI Answer

Answer

6 cm\text{6 cm}

Step-by-step solution

3 steps

b)

  1. Determine the total length of the base of the three cuboids.

    From the previous problem, the length of each cuboid is l=9l = 9 cm.
    When three cuboids are placed side-by-side along their length, the total length of the base is 3l3l.
    Total length of base =3×9 cm=27 cm= 3 \times 9 \text{ cm} = 27 \text{ cm}.

  2. Set up an equation for the total length using the given information about the cylinders.

    The first row has 3 cylinders. Let DD be the diameter of each cylinder.
    The total length occupied by the 3 cylinders is 3D3D.
    There is an equal distance of 4.5 cm on either side of the first row of cylinders.
    So, the total length of the base is the sum of the two gaps and the total diameter of the three cylinders.

    27 cm=4.5 cm+3D+4.5 cm27 \text{ cm} = 4.5 \text{ cm} + 3D + 4.5 \text{ cm}
  3. Solve the equation for DD.

    Combine the constant terms:

    27=9+3D27 = 9 + 3D

    Subtract 9 from both sides:

    27−9=3D27 - 9 = 3D 18=3D18 = 3D

    Divide by 3:

    D=183D = \frac{18}{3} D=6 cmD = 6 \text{ cm}

    The diameter of each cylinder is 6 cm\text{6 cm}.

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