ABCDEF is a jogging track- in which area of the semi-circle BCD is 5000- m 2- If OO- is 100- m- Find the area of the shaded region-A- 20000-3-1- m 2B- 5000-9-1- m 2C- 10000-6-1- m 2D- 100-7-1- m 2

The correct option is C Area(BCD)=5000/πm^2 Radius =π r^2/2=5000/π So, r=100/πm DE = r+ OO' + r =2r+100/π=300/π Area of the shaded region = Area of rectangle A ...

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Standard X

Mathematics

Area of Sector

ABCDEF is a j...

Question

ABCDEF is a jogging track, in which area of the semi-circle BCD is $\frac{5000}{π} m^{2}$ . If OO' is $\frac{100}{π} m,$ Find the area of the shaded region.

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Solution

The correct option is A

Area(BCD)= $\frac{5000}{π} m^{2}$
Radius = $\frac{π r^{2}}{2} = \frac{5000}{π}$
So, $r = \frac{100}{π} m$
DE = r+ OO' + r
$= 2 r + \frac{100}{π} = \frac{300}{π}$
Area of the shaded region = Area of rectangle ABCD - 2(Area of semi-circle BCD)
Area of the shaded region = $\frac{300}{π} \times 2 r - (\frac{10000}{π}) \frac{10000}{π} [\frac{6}{π} - 1] m^{2}$

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ABCDEF is a jogging track, in which area of the semi-circle BCD is 5000πm2. If OO' is 100πm, Find the area of the shaded region.

The correct option is A Area(BCD)=5000πm2 Radius =πr22=5000π So, r=100πm DE = r+ OO' + r =2r+100π=300π Area of the shaded region = Area of rectangle ABCD - 2(Area of semi-circle BCD) Area of the shaded region = 300π×2r−(10000π)10000π[6π−1]m2

ABCDEF is a jogging track, in which area of the semi-circle BCD is $\frac{5000}{π} m^{2}$ . If OO' is $\frac{100}{π} m,$ Find the area of the shaded region.