Question E.10: Problems with Equations Find the radius (r), in centimeters,...
Problems with Equations
Find the radius (r), in centimeters, of a spherical water droplet with a volume (V) of 0.058 \ cm^2 . For a sphere,V = (4 /3)πr^3.
SORT Begin by sorting the information into given and find.
GIVEN: V = 0.058 cm^3
FIND: r in cm
STRATEGIZE Write a conceptual plan for the problem. Focus on the equation(s). The conceptual plan shows how the equation takes you from the given quantity (or quantities) to the find quantity. The conceptual plan may have several parts, involving other equations or required conversions. In these examples, you use the geometrical relationships given in the problem statements as well as the definition of density, d = m / V, which you learned in this chapter.
RELATIONSHIPS USED
V=\frac{4}{3} \pi r^3SOLVE Follow the conceptual plan. Solve the equation(s) for the find quantity (if it is not solved already). Gather each of the quantities that must go into the equation in the correct units. (Convert to the correct units if necessary.) Substitute the numerical values and their units into the equation(s) and calculate the answer. Round the answer to the correct number of significant figures.
SOLUTION
V=\frac{4}{3} \pi r^3
r^3=\frac{3}{4\pi}V
r=\frac{3}{4\pi}V
r=\left(\frac{3}{4\pi}V\right)^{1/3}
r=\left(\frac{3}{4\pi}0.058 \ cm^3\right)^{1/3}
= 0.24013 \ cm
0.24013 \ cm = 0.24 \ cm
CHECK Check your answer. Are the units correct? Does the answer make sense?
The units (cm) are correct, and the magnitude makes sense.