Question

There are two circular gardens A and B. The circumference of garden A is 1.760 km and area of garden B is 25 times the area of garden A. Find the circumference of garden B.​

Answer 1

Step-by-step explanation:

Circumference of garden A = 1.760 Km = 1760 m ( as 1 km = 1000 m )

Circumference = 2πr

so radius of garden a

1760 m = 2 * 22/7 * r

1760 m / 22 / 2 * 7 = r

280 m = r

25(area of garden A) = area of garden B

area of garden A = πr^2

area of garden A = 22/7 * 280 m * 280m

area of garden A = 246400 m^2

25(area of garden A) = area of garden B

246400 m^2 = area of garden B

area = π*r*r

area of garden B =25(π*r*r)

25*π*r*r

25*22/7 * r * r = 246400

r * r = 246400 * 7 / 22 / 25

r = √3136

r = 56 m

circumference of garden B = 2 π r

circumference of garden B = 2 * 22 / 7 * 56

circumference of garden B = 352 m = 0.352 km

Answer 2

Let r be the radius of garden A.

Circumference = 1.760km to m

= 1.760×1/1000m

= 1760m.

Now,

Circumference = 2πr

1760m = 2×22/7×r

r = 1760×7/ 2×22

Therefore,

r = 280m.

So,

Area = πr²

= 22/7×280×280

= 2,46,400m².

Now,

Let R be the radius of garden B.

According to question,

Area = 25 × the area of garden A

πR² = 25 × 2,46,400

R² = 25 × 2,46,400 × 7/22

R² = 1960000

R = √1960000

R = 1400 m.

Therefore,

Circumference of garden B = 2πr

= 2×22/7×1499

= 8800m to km

= 8.8 km.............. answer

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