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What is the angle in degrees made by a sector, the ratio of whose area with the area of the semicircle is equal to 1:10?
- a)36
- b)18
- c)24
- d)9
Correct answer is 'B'. Can you explain this answer?
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What is the angle in degrees made by a sector, the ratio of whose area...
To find the angle in degrees made by the sector, we need to determine the ratio of the area of the sector to the area of the semicircle and then convert it into an angle.
Let's assume the radius of the semicircle is 'r'. Therefore, the area of the semicircle is (πr^2)/2.
Now, let's find the area of the sector. The ratio of the area of the sector to the area of the semicircle is given as 1:10. So, the area of the sector is (1/10) times the area of the semicircle.
Area of the sector = (1/10) * (πr^2)/2
= (πr^2)/20
The angle in radians made by the sector is given by the formula:
Angle in radians = Area of sector / (πr^2)
= [(πr^2)/20] / [(πr^2)/2]
= 1/10
Now, we need to convert the angle in radians to degrees. Since 2π radians is equivalent to 360 degrees, we can set up a proportion:
2π radians = 360 degrees
1/10 radians = x degrees
Cross-multiplying, we get:
x = (1/10) * 360
x = 36 degrees
Therefore, the angle in degrees made by the sector is 36 degrees.
Hence, the correct answer is option (a) 36.
Let's assume the radius of the semicircle is 'r'. Therefore, the area of the semicircle is (πr^2)/2.
Now, let's find the area of the sector. The ratio of the area of the sector to the area of the semicircle is given as 1:10. So, the area of the sector is (1/10) times the area of the semicircle.
Area of the sector = (1/10) * (πr^2)/2
= (πr^2)/20
The angle in radians made by the sector is given by the formula:
Angle in radians = Area of sector / (πr^2)
= [(πr^2)/20] / [(πr^2)/2]
= 1/10
Now, we need to convert the angle in radians to degrees. Since 2π radians is equivalent to 360 degrees, we can set up a proportion:
2π radians = 360 degrees
1/10 radians = x degrees
Cross-multiplying, we get:
x = (1/10) * 360
x = 36 degrees
Therefore, the angle in degrees made by the sector is 36 degrees.
Hence, the correct answer is option (a) 36.
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