Question

If a edge of a cube is doubled

i) How many times will it's surface area will increase ?
ii) how many times will it's volume increase ? ​

Answer 1

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Complete step-by-step answer:

As we know that the cube has 6 sides and each side represents the square.

And the area of square is =(side)2

Let the side length of the cube be a unit.

So the surface area (S.A) of the cube is =6a2 sq. unit

⇒S.A=6a2 sq. unit ………………….. (1)

And we all know that the volume (V) of the cube is =(Side)3

⇒V=a3 unit cube………………………… (2)

Now it is given that the edge of the cube is doubled.

So now the edge of the cube becomes 2a.

So the new surface area (S.A1) of the cube is =6(2a)2=6(4a2)=24a2 sq. unit.

⇒S.A1=4(6a2)

Now from equation (1) we have,

⇒S.A1=4(S.A)

So the new surface area of the cube is four times the old surface area.

And the new volume (V1) of the cube is =(2a)3=8a3

⇒V1=8a3

Now from equation (2) we have,

⇒V1=8(V)

So, the new volume of the cube is eight times the old volume.

So, this is the required answer

Answer 2

Answer:

your answer :

How many times will it's surface area will increase ?

Solution ➡️

Surface area of a cube = 6(side)²

S¹ = 6 ( x )²

= 6x²

Surface area of a new cube = 6 (side)²

= 6 (2x)²

= 6 × 4x²

( S² ) = 24x²

$\frac{ {s}^{1} }{ {s}^{2} } = \frac{ {6x}^{2} }{ {24x}^{2} } \\ \\ \frac{ {s}^{1} }{ {s}^{2} } = \frac{1}{4} \\ \\ { s}^{2} = 4 \: {s}^{1}$

If the edge is doubled then surface area increases 4 times

how many times will it's volume increase ?

let the side of a cube be x cm

volume of a cube = (side)³

( V¹ ) = ( x ) ³ = x³

Now edge of a cube is doubled

i.e New edge 2x

Volume of new cube ( V² ) = ( side )³ = (2x)³ = 8x³

Divide EQ 1 by EQ 2

$\frac{v1}{v2} = \frac{ {x}^{3} }{ {8x}^{3} } \\ \\ \frac{v1}{v2} = \frac{1}{8}$

$v2 = 8v1$

If edge of a cube is doubled then it's volume increases 8 times

Step-by-step explanation:

I hope it helps