Question

A metallic cube with side length $20$ centimeters is melted and made into a rectangular prism of length $40$ centimeters and width $10$ centimeters. What will the height of the rectangular prism be?

• A. $10cm$
• B. $30cm$
• C. $40cm$
• D. $20cm$

Answer 1

The correct option is D $20cm$

Length of the metallic cube,
$s=20cm$
Volume of the cube $=s^3=20\times 20\times 20=8000cucm$

Since this cube is being melted and made into a rectangular prism, the volume of the rectangular prism will be the same as that of the cube.

The dimensions of the rectangular prism are: length $l=40cm$, width $w=10cm$, and height $h=hcm.$
Volume of the rectangular prism$=l\times w\times h=40\times 10\times h=400\times hcucm$
$\Rightarrow 8000=400\times h$

Divide both sides by $400$.
Height of the rectangular prism $=\frac{8000}{400}=20cm$