Question

What's the approximate area of a segment of a circle with a height 6 m and the length of the chord is 20 m? Round your answer to the nearest whole number.

Answer 1

Answer:

Area = 85.4 m^2

Explanation:

Given data:

height h  = 6 m

length l = 20 m

we know that chord length is given as

$chord = 2 \sqrt{ [ height x ( 2 x radius - height) ]}$

$20 m= 2 \sqrt{ [ 6 m x ( 2 x radius - 6 m ) ]}$

solviing for radius r we get

r = 11.33 m

we know that area of segment of circle is given as

$Area =r^2 \times arc cosine [ \frac{r-h}{r}] - (r-h) \times \sqrt{(2\times r\times h - h^2)}$

r - h = 11.33 - 6 = 5.33m

$r^2 = 11.33^2 = 128.44 m^2$

r -h = 11.33 - 6 = 68  m^2

$Area = 128.44 \times arc cosine [\frac{5.33}{11.33}] - 5.33 \times \sqrt{2\times 68 - 36 }$

Area = 85.4 m^2

Answer 2

It would be C. 85.4 Lol your welcome