Maharashtra Board Class 8 Maths part 2 Chapter 16 Surface area and Volume PDF Download

Surface Area And Volume

Let's Recall

Total surface area of a cuboid = 2(l × b + b × h + l × h)

Total surface area of a cube = 6l²

1 m = 100 cm

1 sq m = 100 × 100 sq cm = 10000 sq cm = 10⁴ sq cm

1 cm = 10 mm

1 sq cm = 10 × 10 sq mm = 100 sq mm = 10² sq mm

Let's Learn

Cuboid, cube, cylinder etc are three dimensional solid figures. These solid figures occupy some space. The measure of the space occupied by a solid is called the volume of the solid.

Standard Unit Of Volume

The cube with side 1 cm is shown in the adjoining figure. The space occupied by this cube is a standard unit of volume. It is written as 1 cubic centimeter. In short it is written as 1 cc or 1 cm³.

Activity I

Get some cubes with side 1 cm. Arrange 6 such cubes as shown in figure. We get a cuboid of length 3 cm, breadth 2 cm and height 1 cm. Note that the volume of the cuboid is 3 × 2 × 1 = 6 cc.

Activity II

The length, breadth and height of the adjoining cuboid is 3 cm, 2 cm and 2 cm respectively. In this cuboid there are 3 × 2 × 2 = 12 cubes of volume 1 cc each.

From this we get the formula, volume of a cuboid = length × breadth × height.

Taking l for length, b for breadth and h for height,

Volume of a cuboid = l × b × h

Teacher's Note

Volume means how much space something takes inside. For example, a water tank in your house has a volume—it tells you how many liters of water it can hold.

Exam Trick

Remember: Volume of cuboid = length × breadth × height. Just multiply all three sides together. It is easy!

Points to Remember

Volume measures the space inside a solid shape.
The standard unit of volume is cubic centimeter (cc or cm³).
Volume of cuboid = l × b × h
1 cc means a cube with all sides 1 cm.

Activity III

In the adjoining figure 8 cubes each of volume 1 cc are arranged. By this arrangement we get a cube of side 2 cm. Note that volume of this cube = 2 × 2 × 2 = 2³

From this if the side of cube is l then volume of the cube = l × l × l = l³.

Volume Of Liquid

Space occupied by a liquid in the container is its volume. We know that units used for measuring the volume of liquid are millilitre and litre.

An empty cube of side 10 cm is shown in the adjoining figure.

Its volume = 10 × 10 × 10 = 1000 cc. If this cube is filled with water the volume of water will also be 1000 cc. This volume is called 1 litre.

We know that 1 litre = 1000 millilitre

∴ 1 litre = 1000 cc = 1000 ml, hence 1 cc = 1 ml

The volume of water filled in a cube of side 1 cm is 1 ml.

Teacher's Note

1 litre is the amount of water that fits in a cube of 10 cm on each side. In India, we buy milk and oil in liters at the market.

Exam Trick

Remember: 1 litre = 1000 cc. This is the most important conversion you need to know for exam questions.

Points to Remember

Volume of liquid is measured in millilitre (ml) and litre (L).
1 litre = 1000 ml
1 cc = 1 ml
A 10 cm × 10 cm × 10 cm cube holds exactly 1 litre of water.

Solved Examples

Ex. (1) Find how many litre of water will a cuboidal fish tank contain if its length, breadth and height are 1 m, 40 cm and 50 cm respectively.

Solution: The water contained in the tank is equal to volume of the tank.

Length of tank = 1m = 100cm, breadth = 40cm, height = 50cm.

∴ Volume of the tank = l × b × h = 100 × 40 × 50 = 200000cc,

Volume of water in the tank = 200000 cc = \[\frac{200000}{1000}\] = 200 litre

(∴ 1000 cc = 1l)

∴ Tank will contain 200 litre of water

Ex. (2) The length and height of a cuboidal warehouse is 6m, 4m and 4m respectively. How many cube shaped boxes of side 40 cm will fill the warehouse completely?

Solution: When all the boxes are arranged to fill the warehouse completely the total volume of all boxes equals the volume of the warehouse. To solve the example we will consider the following steps.

(1) Find volume of warehouse

(2) Find volume of a box.

(3) Find the number of boxes

Step (1): Length of warehouse = 6 m = 600 cm, breadth = height = 4 m = 400cm

Volume fo warehouse = l × b × h = 600 × 400 × 400 cc

Step (2): Volume of a box = l³ = (40)³ = 40 × 40 × 40 cc

Step (3): Number of boxes = \[\frac{\text{volume of warehouse}}{\text{volume of a box}}\] = \[\frac{600 \times 400 \times 400}{40 \times 40 \times 40}\] = 1500

∴ 1500 boxes will fill the warehouse completely.

Ex. (3) If 5 litre molten mixture of khoa and sugar is poured in a tray it fills to its full capacity. Find the length of the tray if its breadth is 40 cm and height is 2.5 cm

Solution: To solve the example fill the empty boxes with suitable numbers.

Step (1): Capacity of tray = 5 litre = 5000 cc (∴ 1 litre = 1000 cc)

Step (2): Volume of mixture = 5000 cc

Step (3): Volume of rectangular tray = volume of mixture

l × b × h = 5000 cc

length × 40 × 2.5 = 5000 cc, ∴ length = \[\frac{5000}{100}\] = 50 cm

Teacher's Note

In real life, we use these formulas when we buy a fish tank or storage container. We need to know its volume to understand how much water or material it can hold.

Exam Trick

In problems, if you are given volume and two dimensions, divide the volume by those two dimensions to find the third. For example: volume ÷ length ÷ breadth = height.

Points to Remember

Always change all measurements to the same unit before doing calculations.
Volume of cube = side³ = l³
To find one dimension: Divide volume by the other two dimensions.
1 litre = 1000 cc is important for conversion.

Now I Know

Volume of cuboid = length × breadth × height = l × b × h

Volume of cube = side³ = l³

Practice Set 16.1

1. Find the volume of a box if its length, breadth and height are 20 cm, 10.5 cm and 8 cm respectively.

2. A cuboid shape soap bar has volume 150 cc. Find its thickness if its length is 10 cm and breadth is 5 cm.

3. How many bricks of length 25 cm, breadth 15 cm and height 10 cm are required to build a wall of length 6 m, height 2.5 m and breadth 0.5 m?

4. For rain water harvesting a tank of length 10 m, breadth 6 m and depth 3m is built. What is the capacity of the tank? How many litre of water can it hold?

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