Measurement & Units
What unit is commonly used to measure length in the metric system?
Meters (m)
What is the formula for the area of a rectangle?
Area = Length × Width
What does a scale of 1:100 mean?
1 unit on the drawing = 100 units in real life.
What is an example of a systematic error in measurement?
A ruler that is slightly too short or too long.
What is the first step in solving a multi-step measurement problem?
Identify what is given and what needs to be found.
Convert 4500 mm to meters.
4.5 m
How do you calculate the volume of a rectangular prism?
Volume = Length × Width × Height
A model car is built at a scale of 1:10. If the model is 20 cm long, how long is the real car?
200 cm (or 2 m).
If you measure an object as 12.5 cm but its actual length is 12.8 cm, what is the error?
0.3 cm
Why is it important to check if your answer is reasonable?
To avoid mistakes and confirm accuracy.
What is the difference between area and volume?
Area measures surface (2D), volume measures space occupied (3D).
What shape does this formula apply to: πr²h
Cylinder
If a roof collects 3 L of water per square meter during rainfall, how much water is collected by a 50 m² roof?
150 L
What is the formula for percentage error?
(Measured - Actual) ÷ Actual × 100%
How can you improve the accuracy of a measurement?
Use precise tools, measure multiple times, avoid parallax errors.
What unit would you use to measure the volume of a tank?
Cubic meters (m³) or liters (L).
A composite shape consists of a rectangle and a semicircle. How would you find its total area?
Find the area of each shape separately and add them.
A blueprint drawing shows a length of 5 cm. If the actual length is 10 meters, what is the scale?
1:200 (5 cm = 10 m, so 1 cm = 2 m).
Why might two people measuring the same object get slightly different results?
Human error, different measuring tools, rounding.
If your calculation gives an answer of 23.8 L but the nearest available tank holds 25 L, what should you consider?
Whether the extra capacity is necessary or if a better size exists.
If a measurement is given in square centimeters, how do you convert it to square meters?
Divide by 10,000 (1 m² = 10,000 cm²).
If the volume of a container is 5000 cm³, how many liters does it hold?
5 L (1 L = 1000 cm³).
If a tank is designed to hold twice the volume of another, what is the ratio of their capacities?
2:1
You use a map to measure a building as 30 m, but its actual length is 31.5 m. What is the percentage error?
4.76%
((31.5 - 30) ÷ 31.5) × 100
What makes a mathematical model useful in real life?
It simplifies complex problems, provides estimates, and helps make decisions.