1 Answer

WalterF · Answer 1 · 2023-09-17T16:24:49+0000

We are asked to determine the density of a gulf ball given its mass and volume. To do that, we will use the formula for density:

Where:

$\begin{gathered} D=\text{ density} \\ m=\text{ mass} \\ V=\text{ volume} \end{gathered}$

To determine the volume we will use the fact that the gulf ball can be approximated to a sphere and the volume of a sphere is given by:

$V=(4)/(3)\pi r^3$

Where:

$r=\text{ radius}$

We are given the diameter. We know that the diameter is twice the radius, therefore:

Substituting the value of the diameter we get:

$r=\frac{4.287\operatorname{cm}}{2}$

Solving the operations:

$r=2.144\operatorname{cm}$

Now, we substitute the value of the radius in the formula of the volume:

$V=(4)/(3)\pi(2.144\operatorname{cm})^3$

Solving the operation we get:

$V=41.282\operatorname{cm}^3$

Now, we substitute the value of the volume and the mass in the formula for density:

$D=\frac{45.87g}{41.282\operatorname{cm}^3}$

Solving the operation:

$D=1.11\frac{g}{\operatorname{cm}^3}$

Therefore, the density of the ball is 1.11 g/cm^3.

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