Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
Volume is the total amount of space occupied by a three-dimensional object. Imagine a hollow box; the amount of space inside it that can be filled with air or water is its volume.
The basic unit of volume is the cubic centimeter, written as . Visually, this is a tiny cube where the length, width, and height are all exactly . For larger objects, we use cubic meters ().
A cuboid is a 3D shape like a shoebox or a brick. To find its volume, you must consider three dimensions: Length (how long it is), Breadth (how wide it is), and Height (how tall it is).
A cube is a special cuboid where all sides are equal, like a playing die. Since the length, breadth, and height are the same, we simply multiply the side by itself three times.
Capacity is a term used for the volume of liquids a container can hold. While solid volume is measured in , liquid capacity is measured in Liters () and Milliliters (). Think of a large milk packet as and a small medicine dropper as holding .
The displacement method is used to measure the volume of irregular objects like stones. When you drop a stone into a measuring jar filled with water, the water level rises. The volume of the displaced (risen) water is exactly equal to the volume of the stone.
Weight measures how heavy an object is using units like grams () and kilograms (). In many contexts, of water has a mass of approximately , and (or ) of water weighs approximately .
📐Formulae
💡Examples
Problem 1:
A water tank is in the shape of a cuboid. Its length is , breadth is , and height is . Calculate the volume of water it can hold in and .
Solution:
- Identify the dimensions: , , . \ 2. Use the formula for the volume of a cuboid: . \ 3. Substitute the values: . \ 4. Since , the capacity in is .
Explanation:
We calculate the total space inside the tank by multiplying its three dimensions and then use the direct conversion between cubic centimeters and milliliters.
Problem 2:
A sack of rice weighs and . If a shopkeeper sells and from it, how much rice is left in the sack?
Solution:
- Convert the total weight to grams: . \ 2. Convert the sold weight to grams: . \ 3. Subtract the sold amount from the total: . \ 4. Convert back to : .
Explanation:
To solve weight subtraction problems easily, it is best to convert everything into the smaller unit (grams) first, perform the subtraction, and then convert back to kilograms and grams.