A student measures the volume of 10 identical glass marbles using a measuring cylinder. The student pours 30 cm³ of water into the cylinder, then adds the 1...
Question 1 Report
A student measures the volume of 10 identical glass marbles using a measuring cylinder. The student pours 30 cm³ of water into the cylinder, then adds the 10 marbles. The water level rises to 55 cm³.
(a) State the initial volume of water. [1]
(b) State the final water level. [1]
(c) Calculate the total volume of 10 marbles. [1]
(d) Calculate the volume of one marble. [1]
(e) State why measuring 10 marbles and dividing is better than trying to measure one marble. [1]
Answer Details
(a) Initial volume of water [1]
The student pours 30 cm3 of water into the measuring cylinder before adding the marbles.
Initial volume = 30 cm3 [1]
(b) Final water level [1]
After adding the 10 marbles, the water level rises to 55 cm3. [1]
(c) Total volume of 10 marbles [1]
The marbles displace water equal to their own volume. The volume displaced is the difference between the final and initial readings:
\[ V_{\text{marbles}} = 55 - 30 = 25 \text{ cm}^3 \] [1]This displacement method works because the marbles are solid and do not absorb water, so all the rise in water level is due to the volume of the marbles themselves.
(d) Volume of one marble [1]
\[ V_{\text{one marble}} = \frac{25}{10} = 2.5 \text{ cm}^3 \] [1](e) Why 10 marbles is better than one [1]
A single marble displaces only 2.5 cm3, which is a very small change on the measuring cylinder scale and difficult to read accurately. Using 10 marbles gives a displacement of 25 cm3, which is much easier to read precisely. Dividing by 10 also shares the reading error across all 10 marbles, reducing the uncertainty per marble. [1]
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