Question

The cost of mowing the grass inside of circular lawn at the rate of 0.50 per m 2 is

Rs. 308. Find the cost of fencing the lawn at the rate of Rs. 16 per metre.​

Answer 1

Given :  The cost of mowing the grass inside of circular lawn at the rate of 0.50 per m² is  Rs. 308.

To Find: cost of fencing the lawn at the rate of Rs. 16 per metre

Solution:

Let say Area of circular field  = A  m²

cost of mowing the grass inside of circular lawn of 1 m² = 0.5 Rs

cost of mowing the grass inside of circular lawn of A m² = 0.5A  Rs

cost of mowing the grass inside of circular lawn of A m² = 308  Rs

=> 0.5A = 308

=> A = 616 m²

Area of circle = π R²  = 616

π = 22/7

=> (22/7) R²  = 616

=> R² = 28 * 7

=> R² = 2*2 *7 * 7

=> R = 14  m

Circumference = 2 π R   =  2 (22/7) * 14  = 88 m

cost of fencing the lawn at the rate of Rs. 16 per metre.​

= 88 * 16

= Rs 1408

cost of fencing the lawn = Rs 1408

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Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

For any circle of radius r unit

CIRCUMFERENCE

$\sf{2 \pi r} \: \: unit$

AREA

$\sf{ \pi {r}^{2} \: } \: \: sq \: unit$

GIVEN

The cost of mowing the grass inside of circular lawn at the rate of 0.50 per m^2 is Rs. 308

TO DETERMINE

The cost of fencing the lawn at the rate of Rs. 16 per metre.

CALCULATION

Let radius of the circular lawn = r metre

$\sf{ \: So \: area \: of \: the \: circular \: lawn \: = \pi {r}^{2} \: \: unit}$

Now The cost of mowing the grass inside of circular lawn at the rate of 0.50 per m^2 is

$\sf{Rs. \: \pi {r}^{2} \times 0.50}$

$\displaystyle \: \sf{Rs. \: \: \: \frac{1}{2} \pi {r}^{2} }$

By the given condition

$\displaystyle \: \sf{\: \: \: \frac{1}{2} \pi {r}^{2} = 308}$

$\implies \: \displaystyle \: \sf{\: \: \: \frac{1}{2} \times \frac{22}{7} \times {r}^{2} = 308}$

$\implies \: \displaystyle \: \sf{\: \: \: {r}^{2} = 308 \times 2 \times \frac{7}{22} }$

$\implies \: \displaystyle \: \sf{\: \: \: {r}^{2} = 28 \times 7 }$

$\implies \: \displaystyle \: \sf{\: \: \: {r}^{2} = 4 \times 7\times 7 }$

$\implies \: \displaystyle \: \sf{\: \: \: {r} = 2\times 7 = 14 }$

Now the Circumference of the circular lawn is

$= \sf{ 2\pi \: r\: } \: \: metre$

$= \sf{ 2\pi \times 14\: } \: \: metre$

$\displaystyle \: = \sf{ 2 \times \frac{22}{7} \times 14\: } \: \: metre$

$\displaystyle \: = \sf{ 88 } \: \: metre$

Now the cost of fencing the lawn at the rate of Rs. 16 per metre.

So total cost

$= \sf{ Rs. \: \:( 88 \times 16)\: } \:$

$= \sf{ Rs. \: \: 1408}$

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