Question

if the edge of a cube is doubled, a) by how many times will it's surface area increase b) by how many times will it's volume increase

Answer 1

Working out:

For finding the number of times, the surface area and volume of the cube will increase when the edge is increased can be determined only when we know the formula.

Formula to be known:

• Surface area of cube = 6s²
• Volume of cube = s³

Where, s is the length of side/edge of the cube$.$

Now, let's assume the side length be s and then edge of doubled. So, now the side length is 2s.

(a) Surface area of the cube (s) & (2s)

• Initially = 6s²
• Finally = 6(2s)² = 6(4s²) = 24s²

Here, Final Surface area / Initial surface area = 4, So the surface area of the cube will increase by a Factor of 4✓. Or we can say that, it increases by 300%.

(b) Volume of the cube (s) & (2s)

• Initially = s³
• Finally = (2s)³ = 8s³

So, Final volume / Initial volume = 8, Hence the volume increases by a factor of 8 or increases to its 8 times.✓

And, we're done !!

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