Question

Q.31.In the given figure, OACB is a quadrant of a circle of radius 7 cm. The perimeter of the quadrant is (a) 11 cm (b) 18 cm (c) 25 cm (d) 36 cm​

Answer 1

Given:

In the given figure, OACB is a quadrant of a circle of radius 7 cm. The perimeter of the quadrant is?

To find:

The perimeter of the quadrant is?

Solution:

The radius of the quadrant OACB of a circle, r = 7 cm

We know,$\boxed{\bold{Perimeter\:of\:a\:quadrant = \frac{Circumference \:of\:circle}{4} + (2\times Radius) = \frac{2\pi r}{4} + 2r }}$

Now, by using the above formula, we get

The perimeter of the given quadrant OACB is,

= $\frac{2\pi r}{4} + 2r$

on substituting r = 7, we get

= $\frac{2\times \frac{22}{7} \times 7}{4} + (2\times 7)$

= $\frac{2\times 22}{4} + 14$

= $\frac{44}{4} + 14$

= $11 + 14$

= $\bold{25\:cm}$ ← option (c)

Thus, the perimeter of the quadrant is → 25 cm.

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