Question

A rectangular cardboard of dimension 20 m $\times$ 10 m is placed on a table. 4 squares of side 2.5 m are cut out from the corners and the 4 sides are folded . Find the surface area of the resulting figure which is to be painted on all the sides.

• A. 175 $m^2$
• B. 155 $m^2$
• C. 180 $m^2$
• D. 100 $m^2$

Answer 1

The correct option is A

175 $m^2$

A square of side 2.5 m is cut off from all the corners.
Therefore the length of a rectangular sheet changes to 15 m (20 -( 2 $\times$ 2.5)) and its breadth changes to 5 m(10 - (2 $\times$ 2.5)).

Therefore the surface area of the resulting figure = sum of areas of I, II, III, IV, V
= (15 $\times$ 2.5) + (5 $\times$ 2.5) + (15 $\times$ 2.5) + (5 $\times$ 2.5) + (15 $\times$ 5)
= 175 $m^2$

[Alternatively,
Cutting out squares from the corners and folding the sides results in a cuboid without the top surface, whose dimensions are 15 m × 5 m × 2.5 m
Therefore, area to be painted
= TSA of the cuboid - area of the top surface
= 2 (lb + bh + hl) - lb
= 2 (15×5 + 5×2.5 + 2.5×15) - (15×5)
= 175 sq. m]