We read your photo as:

Recall the relationship between diameter and radius.

Mathematics

ScanSolve AI Answer

Step-by-step solution

6 steps

1.2.1) Calculate the radius of the cylindrical magic cube if the diameter is 67 mm67 \text{ mm}.

  1. Recall the relationship between diameter and radius.

    The radius is half of the diameter.

    Radius=Diameter2\text{Radius} = \frac{\text{Diameter}}{2}
  2. Substitute the given diameter and calculate the radius.

    Radius=67 mm2\text{Radius} = \frac{67 \text{ mm}}{2} Radius=33.5 mm\text{Radius} = 33.5 \text{ mm}

    The radius of the cylindrical magic cube is 33.5 mm\boxed{\text{33.5 mm}}.

    1.2.2) Calculate the total volume of the cylindrical magic cube in mm3\text{mm}^3.
    The following formula may be used:
    Volume of cylinder = π×radius×radius×height\pi \times \text{radius} \times \text{radius} \times \text{height}, where π=3.142\pi = 3.142.

  3. Identify the given dimensions and π\pi value.

    From the image, the height of the cylindrical magic cube is 60 mm60 \text{ mm}.
    From 1.2.1, the radius is 33.5 mm33.5 \text{ mm}.
    The value of π\pi is given as 3.142.

  4. Substitute the values into the volume formula.

    Volume=π×radius2×height\text{Volume} = \pi \times \text{radius}^2 \times \text{height} Volume=3.142×(33.5 mm)2×60 mm\text{Volume} = 3.142 \times (33.5 \text{ mm})^2 \times 60 \text{ mm} Volume=3.142×1122.25 mm2×60 mm\text{Volume} = 3.142 \times 1122.25 \text{ mm}^2 \times 60 \text{ mm} Volume=3.142×67335 mm3\text{Volume} = 3.142 \times 67335 \text{ mm}^3 Volume=211516.47 mm3\text{Volume} = 211516.47 \text{ mm}^3

    The total volume of the cylindrical magic cube is 211516.47 mm3\boxed{\text{211516.47 mm}^3}.

    1.2.3) Calculate the total surface area of the magic cube in mm2\text{mm}^2.
    The following formula may be used:
    Total surface area = side ×\times side ×\times 6

  5. Identify the side length of the cubic magic cube.

    From the image, the side length of the cubic magic cube is 57 mm57 \text{ mm}.

  6. Substitute the side length into the surface area formula.

    Total surface area=side2×6\text{Total surface area} = \text{side}^2 \times 6 Total surface area=(57 mm)2×6\text{Total surface area} = (57 \text{ mm})^2 \times 6 Total surface area=3249 mm2×6\text{Total surface area} = 3249 \text{ mm}^2 \times 6 Total surface area=19494 mm2\text{Total surface area} = 19494 \text{ mm}^2

    The total surface area of the magic cube is 19494 mm2\boxed{\text{19494 mm}^2}.

Was this helpful?

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp