A cuboid is of internal dimensions 60 cm × 54 cm × 30 cm. When 90 uniform small cubes are placed inside it, 80% of the internal volume of the cuboid remains unoccupied. Find the volume and side of the small cubes placed in it.
Answers
Step-by-step explanation:
Question
Answers
Related Questions
A cuboid is of dimensions 60cm, 54 cm, 30 cm. How many small cubes with side 6 cm can be placed in the given cuboid?
Answer
VerifiedVerified
Hint: The volume of the cuboid into which cubes is to be placed is obviously larger than the volume of the cube which is to be placed inside. Division of these volumes will tell about the total number of cubes that can be fitted.
Complete step-by-step answer:
Given dimensions of the cuboid is
Length (l) = 60 cm
Breadth (b) = 54 cm
Height (h) = 30 cm
As we know that the volume (Vcuboid) of the cuboid is =l.b.h
⇒Vcuboid=60×54×30 cm3
Now it is given that the side of the cube is 6 cm.
Now as we know that the volume (Vcube) of the cube is =(side)3.
⇒Vcube=63 cm3.
Now we have to find out how many small cubes with side 6 cm can be placed in the given cuboid.
So in order to find out the number of small cubes (S.C) we have to divide the volume of cuboid to the volume of the cube.
⇒S.C=VcuboidVcube=60×54×306×6×6=10×9×5=450.
Therefore 450 small cubes are placed in the given cuboid.
So this is the required answer.