Estimation in measurements：練習問題

A group of 248 students is going on a field trip. Each tour bus can carry a maximum of 45 passengers. A teacher wants to estimate the number of buses required so that every student has a seat. Which of the following estimation strategies is most appropriate for this context?

A bottle of juice is labeled as having a volume of \(750 \text{ mL}\), correct to the nearest \(10 \text{ mL}\). What is the relative error of this measurement?

In the diagram of a pipe cross-section, the inner radius is measured as \(R_{in} = 5.0 \text{ cm}\) and the outer radius as \(R_{out} = 5.5 \text{ cm}\), both correct to the nearest \(0.1 \text{ cm}\). If the cross-sectional area is \(A = \pi(R_{out}^2 - R_{in}^2)\), find the maximum possible value of \(A\).

A rectangular garden has a measured length of \(12.4 \text{ m}\) and a measured width of \(8.6 \text{ m}\). Both measurements are given correct to the nearest \(0.2 \text{ m}\). Find the maximum absolute error of the calculated area of the garden, correct to 2 decimal places.

The volume of a cube is calculated using a measured side length of \(x = 5.0 \text{ cm}\), which is correct to the nearest \(0.1 \text{ cm}\). If the relative error of the volume is defined as the ratio of the maximum absolute error of the volume to the measured volume, calculate this relative error. (Express your answer in decimal form correct to 3 significant figures).

Round the number \(304,951\) to 3 significant figures.

A distance is measured as \(250\text{ m}\) with a maximum absolute error of \(0.25\text{ m}\). Calculate the relative error of this measurement.

A lift has a weight limit of \(500\text{ kg}\). If \(8\text{ people}\) with an average estimated weight of \(62.4\text{ kg}\) enter, which estimation strategy (rounding up or rounding down) should be used for the weights of the people to ensure they do not exceed the limit? Explain.

A right triangular prism has the following dimensions: a base length of \(6.0 \text{ cm}\), a base height of \(8.0 \text{ cm}\), and a prism length of \(20.0 \text{ cm}\). Each measurement is given correct to the nearest \(0.2 \text{ cm}\).

(a) Find the maximum absolute error of the measurements.
(b) Calculate the upper bound of the volume of the prism.
(c) Find the percentage error of the volume calculated from the measured values, correct to three significant figures.

A solid metal cube has a measured side length of \(5.4\) cm, corrected to the nearest \(0.2\) cm. The density of the metal is measured as \(19.3 \text{ g/cm}^3\), corrected to \(1\) decimal place.

(a) Find the maximum absolute error of the measured side length and the measured density.
(b) Find the upper bound and the lower bound of the mass of the metal cube in grams.
(c) Calculate the maximum percentage error of the mass calculated from the measured values. Give your answer correct to \(2\) decimal places.