Question

1. the sphere shown below is placed in a full overflow cup and sinks to the bottom. how much water is displaced by the sphere? 4.6 cm 51.0 ml 66.5 ml 88.6 ml 407.7 ml

Explanation:

Step1: Find the radius of the sphere

The diameter \(d = 4.6\mathrm{cm}\), and the radius \(r=\frac{d}{2}\). So \(r=\frac{4.6}{2}=2.3\mathrm{cm}\)

Step2: Use the formula for the volume of a sphere

The formula for the volume of a sphere is \(V = \frac{4}{3}\pi r^{3}\). Substitute \(r = 2.3\mathrm{cm}\) into the formula:

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Since \(1\mathrm{cm^{3}} = 1\mathrm{mL}\), the volume of water displaced is equal to the volume of the sphere.

Answer:

\(51.0\mathrm{mL}\) (the third option)