Question

7. If each edge of a cube is doubled,
(i) how many times will its surface area increase?
(i) how many times will its volume increase?​

Answer 1

Answer:-

(i) 4 times

(ii) 8 times

Explanation:-

Let the edge of the cube be 'a'

=>Surface area of a cube = 6a²

=>A = 6a² ----(1) [We are denoting

surface area by 'A']

Now,when the edge of the cube gets doubled i.e. becomes 2a, then A'(new surface area) will be:-

=>A' = 6(2a)²

=>A' = 6(4a²)

=>A' = 24a² ----(2)

Now,on dividing eq.2 by eq.1, we get:-

=>A'/A = 24a²/6a²

=>A'/A = 4

=>A' = 4A

Thus, surface area increases by 4 times.

________________________________

=>Volume of a cube = a³

=>V = a³ ---(1) [We are denoting

volume by 'V']

When edge of the cube gets doubles, then V'(new volume) will be:-

=>V' = (2a)³

=>V' = 8a³ ----(2)

On dividing eq.2 by eq.1, we get:-

=>V'/V = 8a³/a³

=>V'/V = 8

=>V' = 8V

Thus,volume increases by 8 times.

Answer 2

Step-by-step explanation:

Given:

Edge of a cube is doubled.

To find:

•How many times it's surface area increases.

•How many times it's volume increases.

Concept:

A cube is a 3D shape that has all edges same in length.

Solution:

Let the side or edge length be a m.

Then it's Surface area= 6a^2

Now after the edge get doubled it's Surface area=6(2a)^2=24a^2

☆Now area increases by=24a^2/6a^2=4 times.

Now Volume of the cube=a^3

After the edge get doubled= (2a)^3=8a^3

☆Now volume increases by=8a^3/a^3=8 times.