Question

how many square centimeters are in an area of 3.10 in²?
express your answer numerically in square centimeters.
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area = cm²
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part c
convert a volume of 3750 cm³ to cubic meters.
express your answer numerically in cubic meters.
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Explanation:

Step1: Define length conversion factor

1 inch = 2.54 cm

Step2: Derive area conversion factor

Since area is length squared, $1\ \text{in}^2 = (2.54\ \text{cm})^2 = 6.4516\ \text{cm}^2$

Step3: Convert 3.10 in² to cm²

Multiply the given area by the conversion factor:
$3.10\ \text{in}^2 \times 6.4516\ \frac{\text{cm}^2}{\text{in}^2}$

Step4: Calculate the result

$3.10 \times 6.4516 = 19.99996 \approx 20.0$

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Step1: Define length conversion factor

1 meter = 100 cm

Step2: Derive volume conversion factor

Since volume is length cubed, $1\ \text{m}^3 = (100\ \text{cm})^3 = 10^6\ \text{cm}^3$, so $1\ \text{cm}^3 = 10^{-6}\ \text{m}^3$

Step3: Convert 3750 cm³ to m³

Multiply the given volume by the conversion factor:
$3750\ \text{cm}^3 \times 10^{-6}\ \frac{\text{m}^3}{\text{cm}^3}$

Step4: Calculate the result

$3750 \times 10^{-6} = 0.00375$

Answer:

Area conversion: $20.0\ \text{cm}^2$
Volume conversion: $0.00375\ \text{m}^3$