Question

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

Step-by-step explanation:

=6(2a)2=6(4a2)=24a2 sq. unit. So the new surface area of the cube is four times the old surface area. So, the new volume of the cube is eight times the old volume.

Answer 2

★Given:-

• Edge of cube is doubled

★To find:-

• How many times will its surface area increases

• How many times will its volume increases

★Solution:-

Let,

→Edge of cube = s

As the edge of cube is doubled,

→New edge = 2s

We know:

✦Surface area of cube = 6s²

Putting the values,

Original surface area = 6s²

New surface area = 6(2s)²

⇒ 6×4s²

⇒ 4 × 6s²

⇒ 4×original surface area

Hence, when the edge is doubled,its surface area increases by 4 times.

Now,

We know:

✦Volume of cube = (edge)³

Putting the values,

Original volume = s³

Vol of new cube = (2s)³

⇒ 8s³

⇒ 8×s³

⇒ 8×original volume

Hence,when the edge of cube is doubled, the volume increases 8 times.

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