Question

In figure the breadth of the rectangle is 10 units. Two semicircles are drawn on the breadth as diameter. The area of the shaded region is 100 sq. units The shortest distance between the two given semicircles is- D 10 511 units. O 5r units 55 3. units 3- units 4 (0) ㅇ​

Answer 1

The shortest distance between the two given semicircles is  2.5$\pi cm$

Given that;

In the figure, the breadth of the rectangle is 10 units. Two semicircles are drawn on the breadth as a diameter. The area of the shaded region is 100 sq. units

To find;

The shortest distance between the two given semicircles

Solution;

From the figure we have,

AD = 10cm

Therefore radius of the semicircle = 5cm

Thus, the Area of both semicircles = $\frac{\pi 5^{2} }{2} + \frac{\pi 5^{2} }{2}$ = 25$\pi cm^{2}$

Let the width of the rectangle be ' x ' cm

Therefore, the area of the rectangle  = 10x $cm^{2}$

Area of shaded region = Area of the rectangle - Area of both semicircles

Area of shaded region = (10x - 25$\pi )cm^{2}$

Area of shaded region = 100$cm^{2}$ (given)

Therefore,  100$cm^{2}$ = (10x - 25$\pi )cm^{2}$

10x =   100 + 25$\pi$

x = 10 + 2.5$\pi$

Now, the shortest distance between semicircles  = y

y = x - ( 2 x radius of two semicircles)

y =  10 + 2.5$\pi$ - ( 2 x 5)

y = 2.5$\pi cm$

Hence, The shortest distance between the two given semicircles is  2.5$\pi cm$

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Answer 2

Answer:

Step-by-step explanation:

The shortest distance between the two given semicircles is  2.5πcm

Given that;

In the figure, the breadth of the rectangle is 10 units. Two semicircles are drawn on the breadth as a diameter. The area of the shaded region is 100 sq. units

To find;

The shortest distance between the two given semicircles

Solution;

From the figure we have,

AD = 10cm

Therefore radius of the semicircle = 5cm

Thus, the Area of both semicircles = π$\frac{5^2}{2}$+ π$\frac{5^2}{2}$ = 25π$cm^2$

Therefore, the area of the rectangle  = 10x    $cm^2$

Area of shaded region = Area of the rectangle - Area of both semicircles

Area of shaded region = (10x - 25π)$cm^2$

Area of shaded region = 100$cm^2$ (given)

Therefore,  100 = (10x - 25π)$cm^2$

10x =   100 + 25π

x = 10 + 2.5π

Now, the shortest distance between semicircles  = y

y = x - ( 2 x radius of two semicircles)

y =  10 + 2.5π - ( 2 x 5)

y = 2.5πcm

Hence, The shortest distance between the two given semicircles is 2.5πcm

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