Question

.A Gardener walks around a circular park of distance 154 m. If he wants to

level the park at the rate of 25 sq.m . How much amount will he need? (Use

π =

22

7

). ​

Answer 1

Given:

A Gardener walks around a circular park of distance 154 m.

If he wants to  level the park at the rate of 25 sq.m.

To find:

How much amount will he need?

Solution:

Formulas to be used:

$\boxed{\bold{Circumference \:of\:a \:circle = 2\pi r}}\\\\\boxed{\bold{Area \:of\:a \:circle = \pi r^2}}$

The circumference of the circular park = 154 m

Let "r" represents the radius of the circular park.

∴ $2 \pi r = 154$

$\implies 2 \times \frac{22}{7} \times r = 154$

$\implies \bold{r = 24.5 \:m}$

Now,

The area of the circular park is,

= $\frac{22}{7} \times r^2$

substituting the value of r = 24.5 m

= $\frac{22}{7} \times 24.5 ^2$

= $\frac{22}{7} \times 600.25$

= $\bold{1886.50\:m^2}$

If the cost of levelling 1 m² of the circular park = Rs. 25

Then,

The cost of levelling 1886.50 m² is,

= Rs. 25 × 1886.50 m²

= Rs. 47162.50

Thus, the gardener will need → Rs. 47162.50.

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Answer 2

Step-by-step explanation:

Given:

A Gardener walks around a circular park of distance 154 m.

If he wants to level the park at the rate of 25 sq.m.

To find:

How much amount will he need?

Solution:

Formulas to be used:

\begin{gathered}\boxed{\bold{Circumference \:of\:a \:circle = 2\pi r}}\\\\\boxed{\bold{Area \:of\:a \:circle = \pi r^2}}\end{gathered}

Circumferenceofacircle=2πr

Areaofacircle=πr

2

The circumference of the circular park = 154 m

Let "r" represents the radius of the circular park.

∴ 2 \pi r = 1542πr=154

\implies 2 \times \frac{22}{7} \times r = 154⟹2×

7

22

×r=154

\implies \bold{r = 24.5 \:m}⟹r=24.5m

Now,

The area of the circular park is,

= \frac{22}{7} \times r^2

7

22

×r

2

substituting the value of r = 24.5 m

= \frac{22}{7} \times 24.5 ^2

7

22

×24.5

2

= \frac{22}{7} \times 600.25

7

22

×600.25

= \bold{1886.50\:m^2}1886.50m

2

If the cost of levelling 1 m² of the circular park = Rs. 25

Then,

The cost of levelling 1886.50 m² is,

= Rs. 25 × 1886.50 m²

= Rs. 47162.50

Thus, the gardener will need → Rs. 47162.50.