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fredd [130]
3 years ago
9

The radii of two circles are in the ratio of 3 to 1. Find the area of the smaller circle if the area of the larger circle is 27

pi sq. in.
Mathematics
2 answers:
Naddik [55]3 years ago
8 0
ANSWER
3\pi sq.\: in.

EXPLANATION

Let R be the radius of the bigger circle and r, be the radius of the smaller circle.

Then their ratio is given as,

R:r=3:1

We can rewrite it as fractions to get,

\frac{R}{r} = \frac{3}{1}

We make R the subject to get,

R = 3r

The area of the bigger circle can be found using the formula,

Area=\pi {r}^{2}

This implies that,

Area=\pi ({3r})^{2}

Area=9\pi {r}^{2}

But it was given in the question that, the area of the bigger circle is 27π.

27\pi=9\pi {r}^{2}

We divide through by 9π to get,

3 = {r}^{2}

This means that,
r = \sqrt{3}

The area of the smaller circle is therefore

= \pi {( \sqrt{3}) }^{2}

= 3\pi
ololo11 [35]3 years ago
5 0

Answer:

3(pi)

Step-by-step explanation:


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