"Inside the quarter circle are two semi circles...." was answered by students like you

High School
Geometry
High school geometry
Circles

uheaeb56e

Answered question

2022-02-12

Inside the quarter circle are two semi circles. Which has a greater area, A or

Answer & Explanation

moutaccob3jw

Beginner2022-02-13Added 12 answers

Step 1

Area of semicircle $I = P + A$
$= \frac{π {(\frac{r}{2})}^{2}}{2} = \frac{π r^{2}}{8}$ (1)
Area of semicircle - $2 = Q + A$
$= \frac{π {(\frac{r}{2})}^{2}}{2} = \frac{π r^{2}}{8}$ (2)
Wqn (1) and (2) equating,
$P + A = Q + A$
$P + Q$
Area of the quarter of the circle with radius r is $= \frac{π r^{2}}{4}$ (3)
So, $A + B + P + Q = \frac{π r^{2}}{4}$ (4)
Step 2
From eqn (2), we put eqn (2) in eqn (4)
$B + P + \frac{π r^{2}}{8} = \frac{π r^{2}}{4}$
$B + P = \frac{π r^{2}}{8}$ (5)
Compare eqn (1) and eqn (5), we get
$P + A = B + P$
$A + B$
So, both the area of A and B are equal.

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