Question

A cubical box has edge $10$ cm and another cuboidal box is $12.5$ cm long, $10$ cm wide and $8$ cm high. If each edge of the cube and cuboid is doubled, then by how many times will its T.S.A. increase?

Answer 1

(i)Cube:
Total surface area = $6l^2=6\times {10}^2$ = $6\times 100=600m^2$

Cuboid:
Total surface area = $2$(lb + bh + lh)
= $2\left[\right(12.5\times 10)+(10\times 8)+(8\times 12.5\left)\right]$
= $2[125+80+100]$
= $610m^2$

If each edge of the cube is doubled, then,
l = $20$
b =$25$
h =$16$
Then, Cube's Total surface area = $6l^2$
= $6$ x ${20}^2$
= $6$ x $400$
= $2400m^2$

Cuboid:-Total surface area when each side is doubled = $2(lb+bh+lh)$

= $2$[($25$ x $20$) + ($20$ x $16$) + ($16$ x $25$)]

= $2[500+320+400]$= $2\left[1220\right]$

= $2440m^2$

Thus, If each edge of the cube and cuboid is doubled, then its T.S.A will increase $4$ times.