II.2.5. Indirect measurement of the volume
Volume measurement by indirect methods, in the case of bodies with regular geometric shape, is done by measuring linear dimensions and using calculation formulas (in 8th Grade you will learn volume formulas for other geometric bodies):
- For parallelepiped we have the volume formula:
- For the cube we have the volume formula:
The cube is the rectangular parallelepiped with all edges equal. The faces of a cube are square and congruent.
🔓 Solved problems
1. A room has a length of 0.06 hm, a width of 40 dm and a height of 330 cm. Calculate the volume of air in the room in m3.
Solution:
We note the data of the problem and transform the given parameters into SI:
The air being a gas occupies the entire volume of the room. We apply the formula for calculating the volume of a parallelepiped and replace the problem data. Always add the measurement unit to the obtained result.
V = L ∙ l ∙ h = 6 m ∙ 4 m ∙ 3,3 m = 79,2 m3.
2. Pour 500 cm3 of water into a coffee maker to make the coffee. Knowing that a cup of coffee has 150 mL, how many coffees have you made?
Solution:
We note the data of the problem and transform the given parameters into SI:
We divide the volume of the coffee maker by the volume of the cup:
II.2.5.1 Apply what you have learned about indirect measurement of the volume.
🔓 Solved problem
3. Determine the volume of the body in the following image, knowing that only water is placed in the first cylinder, and in the second was added to the water from the first cylinder, the body whose volume you need to determine.
Solution:
🔐 Homework
1. A cube has a side of 5 dm, and a parallelepiped has the following dimensions 800 mm; 0,04 hm and 0,3 dam. Which of the two bodies has the largest volume?
2. Transform into m3:
a) 4.800 dm3 = ? m3
b) 0,06 hm3 = ? m3
c) 53.000 mm3 = ? m3