Volume of Cuboid

Here we will learn how to solve the application problems on Volume of cuboid using the formula.

Formula for finding the volume of a cuboid

Volume of a Cuboid (V) = l × b × h;

Where l = Length, b = breadth and h = height.

1. A field is 15 m long and 12 m broad. At one corner of this field a rectangular well of dimensions 8 m × 2.5 m × 2 m is dug, and the dug-out soil is spread evenly over the rest of the field. Find the rise in the level of the rest of the field.


Formula for Finding the Volume of a Cuboid

The volume of soil removed = The Volume of the Well

                                         = 8 m × 2.5 m × 2 m

                                         = 8 × 2.5 × 2 m3

                                         = 40 m3

Let the level of the rest of the field be raised by h.

Volume of the Cuboid of Dimensions

The volume of the soil spread evenly on the field

                            = Volume of the cuboid of dimensions + Volume of the cuboid of dimensions

                            = 2.5 m × 4 m × h + 12.5 m × 12 m × h

                            = (2.5 m × 4 m × h + 12.5 m × 12 m × h)

                            = (10h + 150h) m\(^{2}\)

                            = 160h m\(^{2}\)

Therefore, 160h m\(^{2}\) = 40 m3

⟹ h = \(\frac{40}{160}\) m

⟹ h = \(\frac{1}{4}\) m

Therefore, the rise in the level = \(\frac{1}{4}\) m

                                            = 25 cm

2. Squares each side 8 cm are cut off from the four corners of a sheet of tin measuring 48 cm by 36 cm. The remaining portion of the sheet is folded to form a tank open at the top. What will be the capacity of the tank?


To make the tank, NGHP has to folded up along NP, LMQK along MQ, EFNM along MN and IJQP.

Capacity of the Tank
The Capacity of the Tank

Now, MN = QP = (48 - 2 × 8) cm = 32 cm, and

NP = MQ = (36 - 2 × 8) cm = 20 cm.

EM = KQ = IP = GN = 8 cm.

Therefore, the capacity of the tank = 32 × 20 × 8 cm3

                                                   = 5120 cm3

                                                   = 5.12 litres [Since, 1 litre = 1000 cm3]

9th Grade Math

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