Question

If each edge of a cube in doubled. (a) how mony times will its surface area increase ?
(b) how many times will its volume increase ?​

Answer 1

Answer:

a) Four times

b) Eight times

Step-by-step explanation:

Given-----> Each edge of cube is doubled

To find----->

a) How many times wii its surface area increase

b) how many times will its volume increase

Solution-----> Let initially edge of cube be x

Surface area of cube ( S₁ ) = 6 ( edge )²

S₁ = 6 ( x )²

S₁ = 6 x²

Volume of cube ( V₁ ) = edge³

V₁ = x³

Now , edge of cube is doubled so,

Edge of new cube = 2x

Now , surface area of new cube ( S₂ )

= 6 ( new edge )²

S₂ = 6 ( 2x )²

= 6 ( 4x² )

S₂ = 24 x²

Volume of new cube = ( New edge )³

V₂ = ( 2x )³

V₂ = 8x³

a) S₂ = 24x²

= 4 ( 6x² )

S₂ = 4 ( S₁ )

It means surface area increase four times .

b) V₂ = 8x³

V₂ = 8 ( V₁ )

It means volume is increased eight times .