Question

if each edge of a cube is doubled how many times will it surface area increase​

Answer 1

Let a cube has an edge x

surface area = 6x²

Doubles the edge,

New edge = 2x

New surface area = 6(2x)² = 24x²

Increase in the surface area = 24x²/6x² = 4 times.

Answer 2

ǫᴜᴇsᴛɪᴏɴ :-

if each edge of a cube is doubled how many times will it surface area increase.

sᴏʟᴜᴛɪᴏɴ :-

Let the edge of cube be x units

then,

➦ Total surface area of cube = 6a² , a = edge

We get,

• Surface Area = 6(x)² = 6x²

If edge is doubled :-

• New edge = 2x units

• Total Surface Area = 6a²

➦ New Surface Area = 6(2x)² = 6 × 4x² = 24x²

Now,

• Increased Areas = New Surface Area / Original surface area

• Area get = 24x² / 6x² = 4 times

Hence,

• The area of cube increases 4 times