for example...
Q. There is a cylinder tube that has a volume of 1 liter and is 12 cm long, what is the diameter of the cylinder?
A. - We know that volume of cylinder = cross sectional area (area of circular base) x length or height
- there are 1000 cubic cm in a liter, therefore our circular base area is 1000/12 = 83.333 square cm.
- from the Area of a circle formula we know that... (pi) x (radius squared) = 83.333 square cm
- we need to solve for the radius; by reverse operation we get radius = the square root of (83.333/pi) = 5.150 cm
- the diameter is twice that of the radius therefore the diameter is 10.3 cm
we have solved a problem using the area of a circle formula!
hope this helps ya
p.s. sometimes it helps to draw a diagram to understand the steps better, just incase there is any trouble.
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Use the formula for the area of a circle: area = pi x radius2 Replace the data you know (in this case the area), and solve for the unknown (in this case the radius).
The formula for finding the area of any circle is pi*radius2..
If the problem gave you the radius, the diameter, or even the circumferenceof the circle, and asked you to find the circle's area, that formula would beexactly what you need.On the other hand, if the problem gave you the area and asked you to find theradius, or the diameter, or even the circumference of the circle, you'd need to usethe area formula, and you'd also probably have to know what you're doing.Finally, if the problem was talking about the amount of money earned in five yearswith compound interest, or the heat dissipated by a 47-ohm resistor with 10 voltsacross it, or the gravitational force on the Earth in the presence of a 10-kilogrammass located 1 meter off of the ground, or the most effective diplomatic approach togetting Iran's nuclear weapons program suspended, then the area of a circle formulawould be completely useless, and would not help at all.
To find the circumference of a circle, you use the formula C = 2∏r. You will need to use this equation to solve for r, the radius. Once you have the radius, you will then plug it into the formula for an area of a circle, which is A = ∏r2. Now, let's fill in your information.C = 2∏r37.14 = 2∏rDivide both sided by 2∏ to isolate the variable r.37.14/2∏ = rSince the original problem uses two decimal places, we will round to two decimal places as well.5.91 = rNow, that we have the radius, 5.91, we can fill it into the formula for an area of a circle to solve your problem.A = ∏r2A = ∏(5.91)2A = ∏(34.94)A = 109.77So, the area of a circle with a circumference of 37.14 is 109.77.
Area formula for circle= --,,- r 2