Question

A square hole of cross - sectional area $4c{m}^2$ is drilled across a cube with its length parallel to a side of the cube. If edge of the cube measures $5cm$, what is the total surface area of the body so formed?

• A. $140c{m}^2$
• B. $142c{m}^2$
• C. $162c{m}^2$
• D. $182c{m}^2$

Answer 1

The correct option is D $182c{m}^2$

Given, cross - sectional area of a square $=4c{m}^2$
$l=5cm$
Surface area of a cube $=6l^2$ $=6(5{)}^2$ $=150c{m}^2$
Total surface area of the cube $=150-2\times 4$ $=142c{m}^2$
Area of the four walls of the hole made parallel to the side of the cube
$=4\times 2\times 5$
$=40c{m}^2$
Total surface area of the body formed $=(142+40)c{m}^2$$=182c{m}^2$