Q: Given a cylinder with a diameter of 2.0 cm and a height of 10.0 cm, what is its volume in $$\mathrm{cm}^3$$? Use $$\pi = 3.14.$$

$$V = \frac{\pi D^2$ h}{4} = \frac{3.14 \times (2.0)^2$ \times 10.0}{4} = 31.4\ \mathrm{cm}^3$$

Q: A rectangular prism has a length of 4.0 cm, width of 3.0 cm, and height of 2.0 cm. What is its volume?

$$V = L \times W \times H = 4.0 \times 3.0 \times 2.0 = 24.0\ \mathrm{cm}^3$$

Q: A student measures the length of an object as 90 cm using hand-spans and 92 cm using a meter stick. What is the relative percent difference between the two measurements?

$$\frac{90 - 92}{(90 + 92)/2} \times 100\% = \frac{-2}{91} \times 100\% \approx -2.2\%$$

Q: Which of the following is the correct formula for calculating the percent error when comparing a measured density to a reference density?

$$\text{percent error} = \frac{\text{measured value} - \text{reference value}}{\text{reference value}} \times 100\%$$

Q: A rectangular prism is measured to have a mass of 48.0 g and dimensions of 4.0 cm × 2.0 cm × 3.0 cm. What is its density?

$$\rho = \frac{48.0}{4.0 \times 2.0 \times 3.0} = \frac{48.0}{24.0} = 2.0\ \mathrm{g/cm}^3$$

Q: A student measures the mass of a cylinder as 22.0 g, its diameter as 2.0 cm, and its height as 7.0 cm. What is the density of the cylinder? (Use $$\pi = 3.14)$$

$$V = \frac{3.14 \times (2.0)^2$ \times 7.0}{4} = 21.98\ \mathrm{cm}^3$$, $$\rho = \frac{22.0}{21.98} = 1.0\ \mathrm{g/cm}^3$$

Question 1

Which of the following best describes the main advantage of using the SI system over anthropometric systems (such as hand-spans or feet) for scientific measurements?

Accepted Answer

The SI system is based on universal, reproducible standards, reducing variability and increasing precision.

Question 2

A student measures the length of a classroom object as 5 hand-spans, with the average hand-span in the group being 18 cm. What is the calculated length of the object in centimeters?

Accepted Answer

$$5 	imes 18 = 90 cm$$

Question 3

Given a cylinder with a diameter of 2.0 cm and a height of 10.0 cm, what is its volume in $$\mathrm{cm}^3$$? Use $$\pi = 3.14.$$

Accepted Answer

$$V = \frac{\pi D^2$ h}{4} = \frac{3.14 	imes (2.0)^2$ 	imes 10.0}{4} = 31.4\ \mathrm{cm}^3$$

Question 4

A rectangular prism has a length of 4.0 cm, width of 3.0 cm, and height of 2.0 cm. What is its volume?

Accepted Answer

$$V = L 	imes W 	imes H = 4.0 	imes 3.0 	imes 2.0 = 24.0\ \mathrm{cm}^3$$

Question 5

If a cylinder has a mass of 66.8 g and a volume of 31.4 $$\mathrm{cm}^3$$, what is its density?

Accepted Answer

$$\rho = \frac{m}{V} = \frac{66.8}{31.4} = 2.13\ \mathrm{g/cm}^3$$

Question 6

A student measures the length of an object as 90 cm using hand-spans and 92 cm using a meter stick. What is the relative percent difference between the two measurements?

Accepted Answer

$$\frac{90 - 92}{(90 + 92)/2} 	imes 100\% = \frac{-2}{91} 	imes 100\% \approx -2.2\%$$

Question 7

Which of the following is the correct formula for calculating the percent error when comparing a measured density to a reference density?

Accepted Answer

$$	ext{percent error} = \frac{	ext{measured value} - 	ext{reference value}}{	ext{reference value}} 	imes 100\%$$

Question 8

A rectangular prism is measured to have a mass of 48.0 g and dimensions of 4.0 cm × 2.0 cm × 3.0 cm. What is its density?

Accepted Answer

$$ho = \frac{48.0}{4.0 	imes 2.0 	imes 3.0} = \frac{48.0}{24.0} = 2.0\ \mathrm{g/cm}^3$$

Question 9

If a measured density for a cylinder is $$2.13\ \mathrm{g/cm}^3$$, which material from the reference table is it most likely made of?

Accepted Answer

Aluminum ($$2.70\ \mathrm{g/cm}^3)$$

Question 10

Which of the following best explains why using a ruler is generally more reliable than using a hand-span for measuring length?

Accepted Answer

A ruler provides standardized, precise units, while hand-spans vary between individuals.

Question 11

A student measures the mass of a cylinder as 22.0 g, its diameter as 2.0 cm, and its height as 7.0 cm. What is the density of the cylinder? (Use $$\pi = 3.14)$$

Accepted Answer

$$V = \frac{3.14 	imes (2.0)^2$ 	imes 7.0}{4} = 21.98\ \mathrm{cm}^3$$, $$ho = \frac{22.0}{21.98} = 1.0\ \mathrm{g/cm}^3$$

Question 12

If the percent error between your measured density and the reference density for aluminum is 20%, what should you conclude about the material of your object?

Accepted Answer

The material is likely not aluminum, since the percent error is greater than 15%.

Question 13

Which of the following is NOT a source of error when measuring the length of an object using a hand-span?

Accepted Answer

The ruler is calibrated to the SI system.

Question 14

A student measures the mass of a rectangular prism as 36.0 g, with dimensions 3.0 cm × 2.0 cm × 2.0 cm. If the reference density for polyvinyl chloride is $$1.39\ \mathrm{g/cm}^3$$, what is the percent error of the student's measurement?

Accepted Answer

$$V = 3.0 	imes 2.0 	imes 2.0 = 12.0\ \mathrm{cm}^3$$, $$ho = \frac{36.0}{12.0} = 3.0\ \mathrm{g/cm}^3$$, $$	ext{percent error} = \frac{3.0 - 1.39}{1.39} 	imes 100\% \approx 116\%$$

Question 15

Which of the following best describes the purpose of calculating the relative percent difference between two measurement methods?

Accepted Answer

To assess the consistency and reliability between the two methods.

Question 16

A student uses a caliper to measure the diameter of a cylinder and a ruler to measure its height. Which of the following best explains why using a caliper is preferred for measuring diameter?

Accepted Answer

A caliper provides more precise and accurate measurements for small distances than a ruler.

Physics 210: Units, Measurements, and Error – Study Guidance

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