객관식
If the density of a certain spherical atomic nucleus is 1.0 x 1014 g/cm3 and its mass is 3.5 x 10-23 g, what is the radius in angstroms? (Å= 10−10 m)
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1. Matter and Measurements
Density of Geometric Objects
Multiple Choice
A copper wire (density = 8.96 g/cm3) has a diameter of 0.32 mm. If a sample of this copper wire has a mass of 21.7 g, how long is the wire?
A
3011 cm
B
3.0 x 103 cm
C
6.0 x 103 cm
D
6022 cm
E
7.41 x 103 cm
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검증된 단계별 안내1
First, convert the diameter of the wire from millimeters to centimeters. Since 1 mm = 0.1 cm, the diameter of the wire is 0.32 mm * 0.1 cm/mm = 0.032 cm.
Next, calculate the radius of the wire by dividing the diameter by 2. The radius is 0.032 cm / 2 = 0.016 cm.
The volume of the wire can be calculated using the formula for the volume of a cylinder: V = πr²h, where r is the radius and h is the height (or length) of the cylinder. Rearrange this formula to solve for h: h = V / (πr²).
To find the volume of the wire, use the density formula: density = mass/volume. Rearrange to find volume: volume = mass/density. Substitute the given values: volume = 21.7 g / 8.96 g/cm³.
Finally, substitute the calculated volume and radius into the rearranged cylinder volume formula to solve for the length of the wire: h = (21.7 g / 8.96 g/cm³) / (π * (0.016 cm)²).
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