The radius of circle A is three feet less than twice the diameter of circle B. If the sum of the diameters of both circles is 49 feet, find the area and circumference of circle …

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asked Apr 1, 2021 200k views

1 Answer

Alex Bush · Answer 1 · 2021-04-08T11:19:26+0000

For this case we have the following system of equations according to the statement:

$r_ {a} = 2d_ {b} -3\\d_ {a} + d_ {b} = 49$

Taking into account that
d = 2r , we can rewrite the second equation as:

$2r_ {a} + d_ {b} = 49$

We have the following system:

$r_ {a} = 2d_ {b} -3\\2r_ {a} + d_ {b} = 49$

We substitute the first equation in the second:

$2 (2d_ {3}) + d_ {b} = 49\\4d_ {b} -6 + d_ {b} = 49\\4d_ {b} + d_ {b} = 49 + 6\\5d_ {b} = 55\\d_ {b} = \frac {55} {5}\\d_ {b} = 11$

Thus, we have:

$r_ {a} = 2d_ {b} -3\\r_a = 2 (11) -3\\r_a = 22-3\\r_ {a} = 19$

Then the area of circle A is:

$A = \pi * (r_ {a}) ^ 2\\A = \pi * (19) ^ 2\\A = 1133.54 \ ft ^ 2$

The circumference is:

$C = 2 \pi * r\\C = 2 * 3.14 * 19\\C = 119.32 \ ft$

Answer:

$A = 1133.54 \ ft ^ 2\\C = 119.32 \ ft$