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.
\boxed{} cm³
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.
\boxed{} ml
(image: black marble with d = 3.0 cm, graduated cylinder with water up to 110 ml (marked 150ml at top, then 140,130,120,110,100,90,80,70,60,50,40,30,20,10))

Explanation:

Step1: Calculate marble volume (sphere)

The marble is a sphere. Formula: $V = \frac{4}{3}\pi r^3$. Radius $r = \frac{d}{2} = \frac{3.0}{2} = 1.5$ cm.
Substitute: $V = \frac{4}{3}\pi (1.5)^3$.
Calculate: $(1.5)^3 = 3.375$, $\frac{4}{3}\pi(3.375) = 4.5\pi \approx 14.14$ cm³ (rounded to ones: 14 cm³).

Step2: Initial water volume (graduated cylinder)

The graduated cylinder shows initial volume at 110 mL (water level at 110).

Step3: Final volume (water + marble)

Final volume = Initial volume + Marble volume (1 mL = 1 cm³).
So, $110 + 14 = 124$ mL.

Answer:

(First blank: Marble Volume; Second blank: Final Volume):
14
124