Question

A metallic cube of edge $2.5$ cm is melted and recasted into the form of a cuboid of base $1.25$ cm $\times 0.25$ cm. Find the increase int the surface area.

• A. $15.625$ $c{m}^2$
• B. $150.625$ $c{m}^2$
• C. $113.125$ $c{m}^2$
• D. $37.5$ $c{m}^2$

Answer 1

The correct option is C $113.125$ $c{m}^2$

Volume of cube$={\left(2.5\right)}^3=2.5\times 2.5\times 2.5=15.625c{m}^3$

Now, volume of cube$=$Volume of cuboid

$\Rightarrow 15.625$$=$$1.25\times 0.25\times h$

$\Rightarrow h=\frac{15.625}{1.25\times 0.25}=50cm$

Initial surface area$=6a^2=6\times {\left(2.5\right)}^2=37.5c{m}^2$

TSA of cuboid$=2(lb+bh+hl)=2(1.25\times 0.25+0.25\times 50+50\times 1.25)$

$=150.625c{m}^2$

$\therefore$Increase in surface area$=150.625-37.5=113.125c{m}^2$