A spherical bass has a diameter of 1.00 inch and a mass of 2.00 grams. Will the ball float or sink water? Remember that if the ball's density if greater than 1.00 g/mL the density of water, the ball will sink. Also remember to use dimensional analysis.

one inch equals 2.54 cm

a mL is the same as a cm³

the volume of the ball (in mL) is
4/3 * π * 1.26³

looks like a floater

To determine whether the ball will float or sink in water, we need to compare its density to that of water.

First, let's calculate the volume of the ball using the diameter provided. The formula for the volume of a sphere is V = (4/3)πr³, where V represents volume and r represents the radius. Since we have the diameter, we can find the radius by dividing the diameter by 2.

Given that the diameter is 1.00 inch, the radius would be (1.00 inch / 2) = 0.50 inches.

Now we can convert the radius from inches to centimeters since we'll be using the metric system for dimensional analysis. We know that 1 inch is equal to 2.54 centimeters.

So, the radius in centimeters would be (0.50 inches * 2.54 centimeters/inch) = 1.27 centimeters.

Now let's calculate the volume of the ball using the given radius. Plugging the radius into the volume formula, we get:

V = (4/3)π(1.27 cm)³ ≈ 10.17 cm³

Now that we have the volume, we can calculate the density of the ball. Density is defined as mass divided by volume. The density of the ball is given as 2.00 grams.

Density = mass / volume = 2.00 grams / 10.17 cm³ ≈ 0.197 g/cm³

Comparing the density of the ball to the density of water (1.00 g/mL or 1.00 g/cm³), we can see that the ball's density is less than that of water. Therefore, the ball will float in water.