Volume of Cube

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

Formula for finding the volume of a cube

Volume of a Cube (V) = (edge)3 = a3;

where a = edge


1. A cubical wooden box of internal dimensions 1 m × 1 m × 1 m is made of 5 cm thick wood. The wood costs Rs. 18600 per cubic metre. If the box is open at the top, find the cost of wood required for making the box.


Volume of Cube Image

Clearly, the outer dimensions of the box are as follows

The outer length = 1 m + 2 × 5 cm = 1.10 m

The outer breadth = 1 m + 2 × 5 cm = 1.10 m

The outer height = Inner height + 5 cm (since, the box is open at the top)

                         = 1.05 m

Therefore, the volume of wood required = Volume of the outer cuboid - volume of the inner cube

                                                          = 1.10 × 1.10 × 1.05 m3 - 13m3

                                                          = 1.2705 m3 - 1 m3

                                                          = 0.2705 m3

Therefore, the cost of wood = 0.2705 × Rs. 18600

                                        = Rs. 5031.30

2. The edge of a cubical block of wood measures 30 cm. A straight cylindrical hole of diameter 10 cm is drilled through the cube. Find the volume of the wood left in the block.


Edge of a Cubical Block

Are of the cross section of the wood block left = Area of a face of the cube of edge 30 cm - Area of a circle of diameter 10 cm.

                                                                   = {302 - π ∙ (\(\frac{10}{2}\))2} cm2

                                                                   = (900 - 25π) cm2.

Cross Section of the Wood Block

Therefore, the volume of the wood left = (Are of the cross section) × Height

                                                         = (900 - 25π) × 30 cm3.

                                                         = (27000 - 750 × \(\frac{22}{7}\)) cm3.

                                                         = \(\frac{172500}{7}\) cm3.

                                                         = 24,642\(\frac{6}{7}\)cm3.

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