Question

the measure of an Arc of a circle is 90 degree and its length is 11 cm what is the diameter of a circle

Answer 1

Answer:

14cm

Step-by-step explanation:

arc angle = 90

circumference of arc =

2 pie r * (90/360)

= 2 (22/7) r /4

= 11r/7

11r/7 = 11 cm

r = 7

diameter = 2*7 = 14cm

Answer 2

The diameter of circle is 14 cm

Solution:

Given that,

The measure of an Arc of a circle is 90 degree

length is 11 cm

The length of arc when central angle given in degrees is:

$Arc\ length = \frac{ \theta }{360} \times 2 \times \pi \times r$

We know that,

$Diameter = 2 \times radius\\\\d = 2r$

Thus the formula becomes:

$Arc\ length = \frac{ \theta }{360} \times \pi \times d\\\\11 = \frac{90}{360} \times 3.14 \times d\\\\44 = 3.14d\\\\d = \frac{44}{3.14}\\\\d = 14.01 \approx 14$

Thus the diameter of circle is 14 cm

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