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.

Question

asked Oct 17, 2021 185k views

1 Answer

Akosky · Answer 1 · 2021-10-23T02:47:15+0000

Answer:

The bowl's diameter is 35.8 cm

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 cm

now, we need to use the formula for the volume of a sphere of radius R:

$Vol=(4)/(3) \pi\,R^3\\24000=(4)/(3) \pi\,R^3\\R^3=(24000\,(3))/(4\,\pi) \\R=\sqrt[3]{(24000\,(3))/(4\,\pi) } \\R\approx 17.894\,\,cm$

therefore, the diameter of the bowl is twice this radius value:

$Diameter\approx 17.894\,* 2=35.788\,\,cm$

this value rounded to 3 significant figures is: 35.8 cm