Question

how many cubes of edge 2 cm can be cut from a 10 cm by 8 cm by 6 cm rectangular prism?

Answer 1

no. of cube edges=n×vol.of cube=vol.of cuboid.

Answer 2

Given,

A rectangular prism, dimensions: 10 cm × 8 cm × 6 cm.

To find,

The Number of cubes of edge 2 cm that can be cut from the prism.

Solution,

Firstly, let the number of cubes that we can cut from the given prism be n.

We can see that the smaller cubes are being cut from the material that has been used to form the prism. It means the total volume of the prism should be equal to the total volume of all the smaller cubes.

Now, the volume of one smaller cube will be

= $(edge)^3$

= (2)³

= 8 cm³.

The volume of the prism

= $l\times b \times h$

= 10×8×6

= 480 cm³.

Since we have assumed a total of n cubes can be cut, so the total volume of n cubes will be

= n×8 cm³

Equating both the volumes, that is,

the total volume of n smaller cubes = volume of the prism

⇒ n×8 = 480

⇒ $n=\frac{480}{8}$

⇒ n = 60 cubes.

Therefore a total of 60 cubes of edge 2 cm can be cut from the given prism.