Question

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Answer 1

20. The circumference of a circle is eight times the circumference of the circle with radius 12 cm. Find its diameter.

There are two circles

The radius of small circle = 12 cm

Circumference of the small circle = 2πr = 2×22/7×12 = 75.42 cm

Now,

according to the question

The circumference of the big circle = 8×circumference of the small circle

= 8×75.42 = 603.36 cm

The circumference of big circle = 2πr

⇒ 603.36 = 2 × 22/7 × r

⇒ 603.36 = 44/7 × r

⇒ 603.36 × 7/44 = r

⇒ 95.98 = r

Now diameter of the big circle = 2 × r = 2 × 95.98 = 191.96 cm

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21. The radii of the two circles are in ratio 3:5. Find the ratio between their circumference.

Let the

radius of the first circle ($\bf r_{1}$) = 3x

radius of the second circle ($\bf r_{2}$) = 5x

Ratio of their circumference is

$\bf =\frac{circumference\: of \:1^{st}\:circle}{circumference \:of\: 2^{nd}\:circle}\\\\=\frac{2\pi r_{1} }{2\pi r_{2}}\\\\= \frac{\cancel{2\pi}\times3 \cancel{x}}{\cancel{2\pi}\times5 \cancel{x}}\\\\= \frac{3}{5}$

= 3:5

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22. The circumference of two circles are in ratio 5:7. Find the ratio between their radii.

Let the

radius of the first circle ($\bf r_{1}$) = 3x

radius of the second circle ($\bf r_{2}$) = 5x

$\bf =\frac{2\pi r_{1}}{2\pi r_{2}} = \frac{5}{7}\\\\=\frac{r_{1}}{r_{2}} = \frac{5}{7}$

Ratio of their radii = 5:7

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23. The perimeter of two square are in ratio 8:15, find the ratio between the length of their sides.

$\frac{4\times side_{1}}{4\times side_{2}}=\frac{8}{15}\\\\\frac{side_{1}}{side_{2}}= \frac{8}{15}$

8:15

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24. The length of the sides of the two squares are in ratio 8:15, find the ratio between their perimeters

let

1st squares side be 8x

2nd square side be 15x

$= \frac{4\times 8x}{4\times 15x}= \frac{8}{15}$

8:15

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25. Each side of a square is 44 cm. find its perimeter. If the perimeter is equal to the circumference of the circle. Find the radius of the circle.

Perimeter of the square = 4 × side

= 4 × 44

= 176 cm

Perimeter of square = circumference of circle

⇒ 176 = 2πr

⇒ 176 = 2 ×22/7 × r

⇒ 176 = 44/7 × r

⇒ 176 × 7/44 = r

⇒ 28 = r

Hence the radius of the circle = 28 cm

Answer 2

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