The reported value for the volume of a rectangular piece of cardboard with the dimensions \(36 \mathrm{cm} \times\) \(20.2 \mathrm{cm} \times 9 \mathrm{mm}\) should be \((\mathrm{a}) \quad 6.5 \times 10^{3} \mathrm{cm}^{3};\) (b) \(7 \times 10^{2} \mathrm{cm}^{3} ;\) (c) \(655 \mathrm{cm}^{3} ;\) (d) \(6.5 \times 10^{2} \mathrm{cm}^{3}\).

Short Answer

Expert verified
The closest reported volume of the rectangular piece of cardboard is \(655 cm^3\).

Step by step solution

01

Convert Units

The first crucial step in this exercise is to convert the unit of measurement for thickness from millimeters to centimeters since the other dimensions are already provided in centimeters. This conversion will ensure that all dimensions are in the same unit which is necessary for accurate calculations. To convert millimeters to centimeters, divide by 10. This implies that 9 mm equals 0.9 cm.
02

Apply the formula for volume

After ensuring all measurements are in the same units, proceed to calculate the volume. The volume (V) of a rectangular object is calculated using the formula \(V = length \times width \times height\). Substitute the provided measurements into this formula: \(V = 36 cm \times 20.2 cm \times 0.9 cm\).
03

Calculate the volume

On performing the multiplication \(36 cm \times 20.2 cm \times 0.9 cm\), you get a volume of 653.52 cubic centimeters. However, this result doesn't match exactly to any of the provided options. Hence, the closest, and thereby, the correct answer should be 655 cubic centimeters.

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