Question

calculating volume
if the diameter of the black marble is 3.0 cm, and by using the formula for volume, what is a good approximation of its volume? record to the ones place.
$\text{______} \text{cm}^3$
determine the initial volume of water in the graduated cylinder. if you added the black marble to the graduated cylinder and it sinks, what final volume should the water level indicate? record to the ones place.
$\text{______} \text{ml}$

Explanation:

Step1: Find the radius of the marble

The radius $r$ of a circle is half of the diameter $d$. Given $d = 3.0$ cm, so $r=\frac{d}{2}=\frac{3.0}{2}=1.5$ cm.

Step2: Calculate the volume of the marble

The volume $V$ of a sphere is given by the formula $V = \frac{4}{3}\pi r^{3}$. Substitute $r = 1.5$ cm into the formula:
\[

$$\begin{align*} V&=\frac{4}{3}\pi(1.5)^{3}\\ &=\frac{4}{3}\pi\times3.375\\ &=4.5\pi\\ &\approx4.5\times 3.14\\ & = 14.13\approx14\text{ cm}^3 \end{align*}$$

\]

Step3: Determine the initial volume of water

From the graduated - cylinder, the initial volume of water $V_{i}=100$ mL.

Step4: Calculate the final volume of water

The final volume $V_{f}$ of water after adding the marble is the sum of the initial volume of water $V_{i}$ and the volume of the marble $V$. So $V_{f}=V_{i}+V$. Since $V_{i} = 100$ mL and $V\approx14$ cm$^{3}$ (and $1$ cm$^{3}=1$ mL), $V_{f}=100 + 14=114$ mL.

Answer:

14
114