A rectangular sheet of lead shielding is placed over the chest of a patient in a dental office while X rays are taken. The sheet measures 65.0 cm by 55.0 cm by 0.30 cm. If the density of lead is 11.3 g/cm3, what is the mass of lead apron?
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To find the mass of the lead apron, we need to multiply the volume of the apron by the density of lead.
1. First, let's calculate the volume of the apron. The volume of a rectangular solid can be found by multiplying its dimensions together:
Volume = length x width x height
Given:
Length (l) = 65.0 cm
Width (w) = 55.0 cm
Height (h) = 0.30 cm
Volume = 65.0 cm x 55.0 cm x 0.30 cm
2. Now, let's convert the volume to the appropriate units. Since the density is given in grams per cubic centimeter (g/cm³), we should convert the length, width, and height to centimeters:
Volume = 65.0 cm x 55.0 cm x 0.30 cm = 1,072.5 cm³
3. Finally, we can use the formula: mass = density x volume.
Given:
Density (ρ) = 11.3 g/cm³
Volume (V) = 1,072.5 cm³
Mass = 11.3 g/cm³ x 1,072.5 cm³
4. Multiply the density by the volume to get the mass:
Mass = 12,095.25 g
Therefore, the mass of the lead apron is 12,095.25 grams.