A spherical bowl of radius r cm is a quarter full when 6 liters of water is poured into it.calculate correct to three significant figures, the diameter of the bowl.
1 answer
Question:
A spherical bowl of radius r cm is a quarter full when 6 liters of water is poured into it.calculate correct to three significant figures, the diameter of the bowl.
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Answer:The bowl's diameter is 35.8 cmStep-by-step explanation:Recall that 1 liter = 1000 cubic cm ad have in mind that in order to get a diameter in cm, we would need to write the volume of the bowl in cubic cm.if 6 liters is 1/4 of the bowl, then 4 times 6 liters must fill the bowl. That is: the volume of the sphere is 24 liters.24 liters in cubic cm is: 24000 cubic cmnow, we need to use the formula for the volume of a sphere of radius R:[tex]Vol=\frac{4}{3} \pi\,R^3\\24000=\frac{4}{3} \pi\,R^3\\R^3=\frac{24000\,(3)}{4\,\pi} \\R=\sqrt[3]{\frac{24000\,(3)}{4\,\pi} } \\R\approx 17.894\,\,cm[/tex]therefore, the diameter of the bowl is twice this radius value:[tex]Diameter\approx 17.894\,* 2=35.788\,\,cm[/tex]this value rounded to 3 significant figures is: 35.8 cm
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