Question

The density of water is 1 gram per cubic centimeter. A more dense object will sink, and a less dense object will float. Will a marble with a radius of 1.4 cm and a mass of 9 grams sink or float in water?

Answer 1

We need to know the density of the marble to know whether it will float or sink. If density is less than 1, it will float. If density more than 1, it will sink

Density  = mass divided by volume

Given:

1. Mass = 9 grams
2. Volume = 11.49 cubic centimeters

Since marble is spherical, we use formula for volume of  sphere

Volume of sphere = $\frac{4}{3}\pi r^{3}$

since r = 1.4, we find the volume of marble:

Volume of marble = $\frac{4}{3}\pi (1.4)^{3}\\=11.49$

Now, finding density:

$D=\frac{mass}{volume}\\D=\frac{9}{11.49}\\D=0.78$

If $D<1$, the object will float.

Since $0.78<1$, the marble will float.

ANSWER: Float

Answer 2

Since the density of the marble is greater than that of water, hence the marble would float.

Density

Density is the ratio of the mass of an object to its volume. A more dense object will sink when placed in water, and a less dense object will float when placed in water.

Given:

Density of water = 1 g/cm³

For the marble:

Volume = (4/3)πr³ = (4/3)π(1.4)³ = 11.49 cm³

Density of marble = 9 g / 11.49 cm³ = 0.79 g/cm³

Since the density of the marble is greater than that of water, hence the marble would float.

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