Question 75
Amrita, during her trek in a Jungle finds a rectangular log of wood measuring 6cm X 12cm X 15cm. She wants to cut this log into exact number of wooden cubes. What is the number of such cubes of equal size that she can get by using the entire log?
Solution
The cube that has to be cut will have a side length equal to the HCF of the sides of the cuboid.
HCF of 6, 12 and 15 is 3, so Amrita can cut cubes of side 3 cm.
Volume of Cuboid = 6*12*15
The volume of one Cube = 3*3*3
Total no. of Cubes = Volume of Cuboid/ Volume of one Cube $$=\dfrac{6\times\ 12\times\ 15}{3^3}=40$$
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