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.

Solution:

$Volume of Cube Image$

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.

Solution:

$Edge of a Cubical Block$

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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