Question

Answer the question below in question

Answer 1

The number of cubes needed are 108.

We have -

A rectangular prism of volume 4 cubic units.

We have to determine -

How many cubes of side 1/3 units are needed to fill the prism completely.

What is th formula to calculate the volume of a cube of side length 'a' units?

The volume of the cube will be -

V = (a x a x a) cubic units

According to question, we have -

Volume of Prism = 4 cubic units.

Assume that the number of cubes of side 1/3 required to fill the prism be x. The volume of x cubes will have to be equal to that of the volume of the prism.

Volume of a cube given = $\frac{1}{3} \times \frac{1}{3} \times \frac{1}{3}$

Then, the Volume of x cubes will be = $\frac{x}{27}$

Equating volume, we get -

$\frac{x}{27} = 4$

x = 27 x 4 = 108

Hence, the number of cubes needed are 108.

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