Question

in the figure above, three congruent circles are tangent to eachother and have centers that lie on the diameter of a larger circle. if the area of each of these small circles is 9pi, what is the area of the larger circle?
a) 36pi
b) 49pi
c) 64pi
d) 81pi

Answer 1

The area of the larger circle is 81π square units.

Congruent circles are circles that are similar in pattern.

The formula for calculating the area of a circle is expressed as:

$A = \dfrac{\pi d^2}{4}$

Given that the area of each of the small circles is 9π, then:

$9 \pi =\frac{\pi d^2}{4}\\9 = \frac{d^2}{4}\\d^2=9*4\\d^2=36\\d=\sqrt{36}\\d=6units$

This shows that the diameter of one of the small circles is 6units.

Since the diameter of the three circles will be equivalent to the diameter of the larger circle, hence;

Diameter of the larger circle = 3(6) = 18units

Get the area of the larger circle:

$A=\frac{\pi D^2}{4}\\A=\frac{\pi \times 18^2}{4}\\A =\frac{324\pi}{4}\\A= 81\pi$

Hence the area of the larger circle is 81π square units.

Learn more on the area of circles here: https://brainly.com/question/12298717