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

Ah clever. So you need two formulas.

1) Volume of the marble.

   4(pi)r^3/3
= 4(pi)(1.4)^3/3
= 11.49 (approx)

2) Formula for density.
  
    D = M / V
        = 9 / 11.49
        = 0.78

0.78 < 1

Therefore the marble will float.

Answer 2

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 $D$, the object will float.

Since $0.78$, the marble will float.

ANSWER: Float