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Dec 25, 2015 · Explanation: The typical area for a circle is: sssA = πr2. Divide both sides by 2, or multiply both by 1 2, to find the formula for half the area: sssA 2 = πr2 2. We can do a practice problem: what's the area of a half a circle (a semicircle) with a radius of 6?
Jan 1, 2016 · π× semi-major axis × semi-minor axis. Explanation: Similar to how the area of a circle is A = πr2, an oval (ellipse) is similar, except for that it has the equivalent of two radii, the semi-minor and semi-major axes. The r2 in the circle area equation is replaced with the product of the lengths of the axes: Aellipse = πab.
The formulas for circumference, area, and volume of circles and spheres can be explained using integration. By adding up the circumferences, 2\pi r of circles with radius 0 to r, integration yields the area, \pi r^2. The volume of a sphere can be found similarly by finding the integral of y=\sqrt {r^2-x^2} rotated about the x-axis.
Mar 3, 2017 · The area of a circle is given by the formula: A = πr2. To see why, you can divide a circle into a number of equal segments and stack them head to tail to form a sort of parallelogram with 'bumpy' sides. The long sides will be about half the circumference in length - that is πr, while the height of the parallelogram will be about r.
Feb 13, 2015 · Sidharth. Feb 13, 2015. We know: Area of a circle = A = (π)r2. Circumference of a circle = C = 2(π)r. Where pi is a constant and r is the radius of the circle. Using these two formulas we can express A in terms of C as follows: C2 = [2(π)r]2. ⇒ C2 = 4[(π)2]r2.
Sep 15, 2015 · Explanation: As you make the segments smaller and smaller, the parallelogram becomes more of a rectangle with shorter side equal to the radius of the circle r and longer side πr - half of the circumference of the circle. Hence we get the formula πr2 for the area of a circle of radius r. If you divide a circle into a number of equal segments ...
Mar 17, 2018 · This finds the rate at which an area is increasing/decreasing, by finding the derivative of the appropriate area formula in respect to time. For explanation sake, here is an example: Let's say we need to find the rate in which the area of a circle is increasing, when the rate of the radius increasing is 2m/s with the radius being at 4 meters ...
Aug 1, 2015 · Explanation: When a circle is completely inscribed within a circle, the radius of that particular circle is half the side of the square. So in this case: The radius: r = 4 2 = 2cm (assuming the unit to be in cm) Area of a circle is given by formula: πr2. Where π is of constant value 3.14. So, area πr2 = 3.14 ⋅ (2)2.
Dec 30, 2015 · If given the area: The normal area of a circle is A=pir^2. Since a semicircle is just half of a circle, the area of a semicircle is shown through the formula A=(pir^2)/2. We can solve for r to show an expression for the radius of a semicircle when given the area: A=(pir^2)/2 2A=pir^2 (2A)/pi=r^2 r=sqrt((2A)/pi) If given the diameter: The ...
Dec 19, 2017 · Its surface area is 4pir^2. Just like radian, where for angle we divide arc size by r to get angle in radians, we can say that the entire surface area of the sphere subtends a solid angle of (4pir^2)/r^2=4pi steradians at the center. We can say that the angle subtended by a surface area A at a distance of r is A/r^2 steradians. Hence, a solid ...
