The radius of a circle of area A and circumference C is doubled.
A)Find the new area of the circle in terms of A .
B)Find the new circumference of the circle in terms of C.
I don’t know how to do this, I’m not used to not having numbers!
2 Answers
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Hi, CG.
We’ll call the old radius r and the new radius r’ (“r-prime”).
We’re told that the radius is doubled. Thus, r’ = 2r (2 times r).
A) The area of a circle is π × (radius)²
So, the area of the old circle, A = πr²
Use the same formula to get the area of the new circle (let’s call it A’)
A’ = π × (r’)² = π × (2r)² = π × 2² × r² = 4 × πr²
Looking at the expression for A, we can substitute into the expression for A’ and get:
A’ = 4A. Thus the new area of the circle is 4 times the old area.
B) Circumference of a circle is 2π × (radius)
Thus, the old circumference is:
C = 2πr
And the new circumference is:
C’ = 2πr’ = 2π × (2r) = 4πr = 2 × 2πr
Substitute in the equation for C:
C’ = 2C
Thus, the new circumference is 2 times the old circumference
Source(s): Ph.D. in chemical engineering -
Circumference equals pi cases the diameter of the circle. subsequently on your question C=10pi centimeters. component of a circle is pi cases the radius squared. subsequently on your question A=25pi sq. centimeters.
