Question

the diameter of a circular park is 84 m. a 3.5 m wide road is constructed outside and around it. find the cost of constructing the road at rupees 20 per m square. take pie value as 22/7

please answer fast I can't understand it ​

Answer 1

Given

• Diameter of a circular park is 84m.
• A 3.5 m wide road is constructed outside and around it.
• Cost of constructing the road at rupees 20 per m square.

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To find

• Cost of constructing the road.

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Solution

• In this question, we have two circles with inner radius (r) = 42m and outer radius (R) = 42 + 3.5 = 45.5m.

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Formula used

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$\dag{\boxed{\boxed{\bf{Area_{(Circle)} = πr^2}}}}$

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• Area of smaller circle

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$\tt:\implies\: \: \: \: \: \: \: \: {Area_1 = \pi r^2}$

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$\tt:\implies\: \: \: \: \: \: \: \: {Area_1 = \dfrac{22}{\cancel{7}} \times \cancel{42} \times 42}$

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$\tt:\implies\: \: \: \: \: \: \: \: {Area_1 = 22 \times 6 \times 42}$

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$\frak:\implies\: \: \: \: \: \: \: \: {\underline{\boxed{\purple{Area_1 = 5,544\: m^2}}}}$

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• Area of larger circle

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$\tt:\implies\: \: \: \: \: \: \: \: {Area_2 = \pi R^2}$

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$\tt:\implies\: \: \: \: \: \: \: \: {Area_2 = \dfrac{22}{\cancel{7}} \times \cancel{45.5} \times 45.5}$

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$\tt:\implies\: \: \: \: \: \: \: \: {Area_2 = 22 \times 6.5 \times 45.5}$

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$\frak:\implies\: \: \: \: \: \: \: \: {\underline{\boxed{\purple{Area_2 = 6,506.5\: m^2}}}}$

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Now,

☆ $\bf{Area_{(Road)} = Area_2 - Area_1}$

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$\tt\longmapsto{Area_{(Road)} = 6,506.5 - 5,544}$

$\tt\longmapsto{Area_{(Road)} = 962.5\: m^2}$

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• It is given in the question that the cost of constructing the road is Rs.20 per m².

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$\tt:\implies\: \: \: \: \: \: \: \: {Total\: cost = Rs. 962.5 \times 20}$

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$\tt:\implies\: \: \: \: \: \: \: \: {Total\: cost = Rs.19,250}$

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Hence,

• The total cost of constructing the road is Rs.19,250.

Answer 2

Answer:

Correct Question:-

1. A circular park, 24 m in diameter, has a path 3.5 m wide running round it on the outside. Find the cost of gravelling the path at Rs.20 per m².

Solution:-

d = 24 m

Area of Park = πr²

$= \frac{22}{7} \times \frac{24}{2} \times \frac{24}{2} \\ = \frac{11 \times 24 \times 24}{14}$

$\rm{Area \: of \: path:-} \frac{11×24×24}{14} -π(12.35)² \\ = \frac{11×12×24}{7} - \frac{22}{7} (8.5)² \\= \frac{22}{7} [144-72.25] \\ = \frac{22×71.75}{7} =225.5² \\ \rm{Cost}=225.5×20 \\ =Rs \: 4510$

Required answer:-

• Rs 4510