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} = a^{3};
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:
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 m^{3} - 1^{3}m^{3}
= 1.2705 m^{3} - 1 m^{3}
= 0.2705 m^{3}
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:
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.
= {30^{2} - π ∙ (\(\frac{10}{2}\))^{2}} cm^{2}
= (900 - 25π) cm^{2}.
Therefore, the volume of the wood left = (Are of the cross section) × Height
= (900 - 25π) × 30 cm^{3}.
= (27000 - 750 × \(\frac{22}{7}\)) cm^{3}.
= \(\frac{172500}{7}\) cm^{3}.
= 24,642\(\frac{6}{7}\)cm^{3}.
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