Question

If each edge of a cube is doubled :
1. How many times will it's surface increase?

2.How many times will it's volume increase?

Answer with explanation pls​

Answer 1

Step-by-step explanation:

let us consider a cube with edge "a".

Therefore,

$surface \: area \: = \: 6 \times {edge}^{2} = 6 \times {a}^{2} \: = 6 {a}^{2} \\ \\ \: volume \: = {edge}^{3} = {a}^{3}$

So according to the question, if we doubled the edge of the cube i.e. 2a.

so,

$surface \: area \: of \: new \: cube \: = 6 \times {(2a)}^{2} = 6 \times 4 {a}^{2} = 24 {a}^{2} \\ \\ volume \: of \: new \: cube \: = {2a}^{3} = 8 {a}^{3}$

So if the edge of the original cube is doubled the surface area and volume of the new cube is 4 and 8times the original cube respectively.