Q15. - Geometry

Question

If the edge of a cube is doubled, the total area is multiplied by ___ and the volume is multiplied by ___.

Step-by-Step Solution

Answer

If the edge of a cube is doubled, the total area is multiplied by four and the volume is multiplied by eight.

Step 1. Given information.

The edge of a cube is doubled.

Step 2. Write the concept.

The lateral area of the cube is given by:

$\text{L.A.}=4e^2$

Where e is the length of the cube.

 The total area of the cube is given by:

$\text{T.A.}=6e^2$

 The volume of rectangle is given by:

$\text{V}=e^3$

Step 3. Explanation.

If the edge of a cube is doubled then the lateral area is multiplied by four and then total area is multiplied by four and the volume multiply by the eight.