Question

The diameters of two circles are in ratio 3:2. Find the ratio of their areas.
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Answer 1

Answer:

Step-by-step explanation:

ANSWER:-

Given:-

• Two circles in the diametrical ratio of 3:2
• We need to find the ratio of their areas.

Concept:-—

Circles and its area

Let's Do!

So, what we need is the relation between Diameter and Radius.

$\rm{Diameter = \dfrac{Radius}{2}}$

So, we can assume a ratio constant as x.

• Diameter of 1st circle is 3x
• Diameter of 2nd circle is 2x

So, accordingly, we can say:-

1. Radius of first circle is 3x/2
2. Radius of 2nd circle is 2x/2 = x

Now, we need to know

$\sf{Area \ of \ Circle = \pi \times r^2}$

So, for 1st circle, we can write

$\sf{Area \ of \ Circle = \pi \times (\dfrac{3x}{2})^2}$

$\sf{Area \ of \ Circle = \pi \times \dfrac{9x}{4}r^2}$ -------------------(1)

Now, area of 2nd circle,:-

$\sf{Area \ of \ Circle = \pi \times (x)^2}$

$\sf{Area \ of \ Circle = \pi \times x^2}$------------------(2)

Connecting (1) and (2) in fractions, pi gets cancelled, x^2 gets cancelled,

$\dfrac{\dfrac{9}{4}}{\dfrac{1}{1}}$

So, area ratio is 9:4, after simplifying.

Answer 2

Answer:

πr

2

2

πr

1

2

Explanation: