An open box is made by cutting the congruent squares from the corners of a rectangular sheet of cardboard of dimension 20 cm × 15 cm. If the side of each square is 2 cm, the total outer surface area of the box is :
a) 148 cm2
b) 284 cm2
c) 316 cm2
d) 460 cm2
Answer: b
Explanation: Clearly,
$$l$$ = (20 – 4) cm = 16 cm
b = (15 – 4) cm = 11 cm and
h = 2 cm
Outer surface area of the box :
$$\eqalign{
& = \left[ {2\left( {l + b} \right) \times h} \right] + lb \cr
& = \left[ {\left\{ {2\left( {16 + 11} \right) \times 2} \right\} + 16 \times 11} \right] \cr
& = \left( {108 + 176} \right) \cr
& = 284{\text{ c}}{{\text{m}}^2} \cr} $$
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