Question

The ratio of radii of two circles is 4:5. Find the ratio of their areas. *

16:25

15:50

12:30

42:69

​

Answer 1

Given that,

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• The Ratio of radii of two circles is 4:5.

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☯ Let the radius of the circle be 4x and 5x. And, their area be $\sf A_1$ and $\sf A_2.$

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Therefore,

$:\implies\sf A_1 = \pi r^2 \\\\\\:\implies\sf A_1 = \pi \Big(4 x \Big)^2\\\\\\:\implies\sf A_1 = 16 \pi x^2$

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Now,

$:\implies\sf A_2 = \pi r^2 \\\\\\:\implies\sf A_2 = \pi \Big(5 x \Big)^2\\\\\\:\implies\sf A_2 = 25 \pi x^2$

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• The ratio of their areas is:

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$:\implies\sf \dfrac{Area_{1}}{Area_{2}} = \Bigg( \dfrac{16 \: \cancel{ \pi x^2}}{25 \: \cancel{ \pi x^2}} \Bigg) \\\\\\:\implies\sf \dfrac{Area_{1}}{Area_{2}} = \dfrac{16}{25} \\\\\\:\implies{\underline{\boxed{\frak{\purple{Ratio = 16:25}}}}} \:\bigstar$

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$\therefore\;{\underline{\sf{Hence, \ the \ ratio \ of \ their \ areas \ is \ {\textsf{\textbf{Option a) 16:25}}}.}}}$

Answer 2

Question

The ratio of radii of two circles is 4:5. Find the ratio of their areas. *

16:25

15:50

12:30

42:69

Answer

Let, radius of one circle be 4x

radius of another circle be 5x

Ratio of their areas

$= (\frac{area_{1}}{area_{2}}) \\ = (\frac{\pi {r}^{2}_{1}}{\pi {r}^{2}_{2}}) \\ = (\frac{16 {x}^{2} }{25 {x}^{2} }) \\ = \frac{16}{25}$

$\frac{area_{1} }{area_{2} } = \frac{16}{25} = \: 16:25$

More Information

Surface Area of Cuboid = 2(lb+bh+lh)

Surface Area of Cube = 6(side)²

Area of four walls = 2(l+b)h

Lateral Surface Area of Cuboid = 2(l+b)h

Lateral Surface Area of Cube = 4(side)²