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Area under the circle x2 + y2 = 16 is
- a)π sq units
- b)13π sq units
- c)16 π sq units
- d)4 π sq units
Correct answer is option 'C'. Can you explain this answer?
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Area under the circle x2+ y2= 16 isa) sq unitsb)13 sq unitsc)16 sq un...
Finding the Area under a Circle
Given the equation of the circle x^2 + y^2 = 16, we need to find the area under the circle.
Solution:
- Rewrite the equation of the circle in terms of y:
y^2 = 16 - x^2
- Take the square root of both sides:
y = ± √(16 - x^2)
- We are only concerned with the positive square root since we are finding the area under the circle, which is above the x-axis.
- Plot the graph of y = √(16 - x^2) from x = -4 to x = 4 (the limits of the circle) to see the shape of the area we are finding.
- We notice that the area under the curve is a quarter of a circle with radius 4.
- The area of a quarter circle with radius r is (πr^2)/4.
- Substituting r = 4, we get:
Area = (π(4)^2)/4 = 16π/4 = 4π
- The exact value of π is irrational, but we can approximate it to 3.14.
- So, the area under the circle is approximately:
Area ≈ 4(3.14) = 12.56
- However, the question asks for the exact area, which is:
Area = 4π = 12.57 sq units
Therefore, the correct option is "C" - 16 sq units.
Given the equation of the circle x^2 + y^2 = 16, we need to find the area under the circle.
Solution:
- Rewrite the equation of the circle in terms of y:
y^2 = 16 - x^2
- Take the square root of both sides:
y = ± √(16 - x^2)
- We are only concerned with the positive square root since we are finding the area under the circle, which is above the x-axis.
- Plot the graph of y = √(16 - x^2) from x = -4 to x = 4 (the limits of the circle) to see the shape of the area we are finding.
- We notice that the area under the curve is a quarter of a circle with radius 4.
- The area of a quarter circle with radius r is (πr^2)/4.
- Substituting r = 4, we get:
Area = (π(4)^2)/4 = 16π/4 = 4π
- The exact value of π is irrational, but we can approximate it to 3.14.
- So, the area under the circle is approximately:
Area ≈ 4(3.14) = 12.56
- However, the question asks for the exact area, which is:
Area = 4π = 12.57 sq units
Therefore, the correct option is "C" - 16 sq units.
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Area under the circle x2+ y2= 16 isa) sq unitsb)13 sq unitsc)16 sq unitsd)4 sq unitsCorrect answer is option 'C'. Can you explain this answer?
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