Question

A garden is 150 m long and 120 m wide. There are two circular skating floors with radii equal to 35 m and 28 m in the garden. Find the cost of covering the remaining portion of the garden with grass at the rate of Rs. 1.25 per sq. m.

Answer 1

Answer:

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Answer 2

Before, finding the answer. Let's find out on how we can find the answer.

• First, we must find the area of garden by using the formula of

$\boxed{ \sf \: Area \: of \: Rectangle = l \times b}$

• Next, we must find the Area of Circle of both the Circular Skating floors using the formula of

$\boxed{ \sf \: Area \: of \: Circle =\pi r^{2} }$

• Now, we must add both the Area of Circle and subtract from Area of Rectangle.
• At last, we must multiply with the cost.

________________________

Given :

• Length & Breadth of Rectangle = 150 and 120 m
• Radii of Circle = 35 m and 28 m
• Rate = Rs. 1.25 per sq.m

To find :

• Cost of Covering with Grass of remaining portion.

Solution :

Area of Garden = length × breath

= 150 × 120 sq.units

= 18000 sq.m

Hence, the Area of Garden is 18000 sq.m.

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Area of Circular Skating Floor = πr²

Here,

• π is 22/7
• r is radius

$\sf Area \: of \: first \: Circle = \dfrac{22}{7} \times 35 \times 35$

$\sf \: = \dfrac{22}{7} \times 1225$

$\sf = \dfrac{26950}{7} m^{2}$

$\sf = 3850 \: m^{2}$

Hence, the Area of first Circle is 3850 m².

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Area of Circle is πr².

$\sf Area \: of \: second\: Circle = \dfrac{22}{7} \times 28 \times 28$

$\sf = \dfrac{22}{7} \times 784$

$\sf \: = \dfrac{17248}{7} {sq.units}^{2}$

$\sf = 2464 \: m^{2}$

Hence, the Area of Second Circle is 2464 m².

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Total Area of Circle = Area of Circle 1 + Area of Circle 2

= 3850 + 2464 m²

= 6314 m²

Hence, Total Area of Circle is 6314 m².

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Remaining Area = 18000 - 6314 m²

= 11686 m²

Hence, the Remaining Area is 11686 m².

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Cost of Grass = rate × remaining area

= 1.25 × 11686

= Rs. 10,107

Hence, the Rate for Grass is Rs. 10107.