Question

Pavan has a piece of wire and he wants to make some geometrical figures with it. Which of the following geometrical figures can he make with the minimum length of wire?

• A. All require the same length of wire
• B. Fig. ii
• C. Fig. i
• D. Fig.iii

Answer 1

The correct option is C Fig. i

Fig. (i)

Perimeter = πr + 2r
$=\frac{22}{7}\times 1.4+2.8=7.2cm$

Fig. (ii)

Perimeter = Perimeter of square + Perimeter of circle

$Perimeter=4\times 2.8+2\times \frac{22}{7}\times 1.4=11.2+8.8=20cm$

Fig. (iii)

Perimeter = Perimeter of arc + Perimeter of slant heights

$Perimeter=\frac{22}{7}\times 1.4+2+2=8.4cm$

Therefore, fig. (i) will require less wire.