Question

A certain quality of wood costs ₹ 250 per m³. A solid cubical block of such wood is bought for ₹ 182.25. Calculate the volume of the block and use the method of factors to find the length of one edge of the block.

Answer 1

Given: A certain quality of wood costs ₹ 250 per m³ and a solid cubical block of such wood is bought for ₹ 182.25.

Step-wise calculation:

1. Volume of the block (in m³)

= Cost paid ÷ Cost per m³

= 182.25 ÷ 250

= 0.729 m³

2. Write 0.729 as a fraction and factor:

`0.729 = 729/1000`

729 = 3⁶ and 1000 = 10³ 

= (2·5)³

So a³ = 0.729 

= `3^6/10^3` 

= `(3^2)^3/(10)^3`

3. Take cube root (method of factors):

a = cube root (a³) 

= cube root `[(3^2)^3/10^3]` 

= `3^2/10` 

= `9/10`

= 0.9 m

4. Convert to centimetres if desired:

0.9 m = 90 cm

Volume = 0.729 m³.

Length of one edge = 0.9 m = 90 cm.