Question

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

Answer 1

Answer:

4 times

8 times

Step-by-step explanation:

let the side of cube be x

then if it is doubled them it will be 2x

we know that surface area if the cube is

$6{x}^{2}$

if it is doubled then

$6( {2x}^{2}) \\ = 4 \times 6 {x}^{2 } \\ = 4times$

for volume formula is x^3

for cube of side 2x

then volume would be (2x)^3

=8*(x)^3

= 8 times

Answer 2

Answer:

if , the edge of the cube is = x

then age of the new cube when it is doubled = 2x

surface area of the first cube = 6a²

                                                  =6x²

surface area of the new cube = 6a²=6*(2x)²=6*4x²

                                                 = 24x²

so, on comparing the ratio of their surface area we get,.......

surface are of first cube/surface area of new cube=6x²/24x²=1/4=1:4

means that ..the  new cube will have Four times more surface area than the first cube.

BUT , on other hand if we compare the volumes ,,

volume of the first cube = a³=x³

volume of the new cube when we doubled its edge=(2x)³=8x³

so ratio of the first cube to the new cube is = x³/8x³=1:8

so volume of the cube will increase 8 times on doubling the age....

(i)  surface area will  be increased four times

(ii) volume will be increased eight times

Step-by-step explanation: