Final answer:
To find the mass of the wood board, convert its height from mm to cm, calculate the volume in cubic centimeters, and then multiply by the density, which yields a mass of 19.7 grams when rounded to the correct significant figures.
Step-by-step explanation:
To calculate the mass of the wood board, we need to use its density and the dimensions provided to find its volume. The formula for density is mass divided by volume (density = mass/volume), which can be rearranged to find mass (mass = density × volume). Remember to convert all measurements to the same unit; here we convert height from mm to cm before calculating the volume. We multiply the density by the volume to find the mass.
First, convert the height from millimeters to centimeters:
10.67 mm × (1 cm / 10 mm) = 1.067 cm
Next, calculate the volume of the board:
Volume = length × width × height
Volume = 4.94 cm × 5.45 cm × 1.067 cm = 28.579 cm³
Now calculate the mass of the board:
Mass = density × volume
Mass = 0.687 g/cm³ × 28.579 cm³ = 19.654 g
Considering significant figures, the volume has three significant figures and the density also has three significant figures; therefore, the final mass should be rounded to three significant figures:
Mass = 19.7 g