Question

A road 14 m wide surrounds a circular park whose circumference is 704m. Find the area of the road​

Answer 1

Answer:

• Hint: First, before proceeding for this, we must draw two concentric circles with inner circle representing the circular park whose circumference is given and outer circle represent the circle made by extending the road by 14m from the inner circle. Then, we are given the question that the inner circle has the circumference of 704m and we also know that the circumference C of the circle with radius r is given by C=2πr. Then, we also know from the study of circles that area A of the circle with radius r is given by A=πr2, using both circles, we get the desired results.

• Complete step-by-step answer:
• Complete step-by-step answer:In this question, we are supposed to find the surface area of the road and cost of paving it at a cost of Rs. 100 per metre square when the road, 14m wide, surrounds a circular park whose circumference is 704m.
• Complete step-by-step answer:In this question, we are supposed to find the surface area of the road and cost of paving it at a cost of Rs. 100 per metre square when the road, 14m wide, surrounds a circular park whose circumference is 704m.So, before proceeding for this, we must draw two concentric circles with inner circle representing the circular park whose circumference is given and outer circle represent the circle made by extending the road by 14m from inner circle as:
• Then, we are given in the question that inner circle has the circumference of 704m and we also know that the circumference C of the circle with radius r is given by:

C=2πr

C=2πrThen, by substituting the value of C from the question which is 704, we get the value of inner radius r as:

C=2πrThen, by substituting the value of C from the question which is 704, we get the value of inner radius r as:704=2×22/7×r

⇒r=704×7/2×22

2×22

2×22 ⇒r=112

• So, we get the radius of the inner circle as 112m.
• So, we get the radius of the inner circle as 112m.Then we also know from the study of circles that area A of the circle with radius r is given by:
• So, we get the radius of the inner circle as 112m.Then we also know from the study of circles that area A of the circle with radius r is given by:A=πr2
• So, we get the radius of the inner circle as 112m.Then we also know from the study of circles that area A of the circle with radius r is given by:A=πr2So, by substituting the value of r calculated above as 112m in the area formula to get the area A1 of inner circle as:
• A1=π(112)2
• A1=22/7×112×112
• A1=39424
• So, we get the area of the inner circle as 39424 meter square.
• So, we get the area of the inner circle as 39424 meter square.Then, by using the same formula for outer circle but its radius R becomes the summation of the inner radius and the road width as:
• R=r+14
• R=r+14⇒R=112+14
• R=r+14⇒R=112+14⇒R=126

Now, by substituting the value of R calculated above as 126m in the area formula to get the area A2 of outer circle as:

Now, by substituting the value of R calculated above as 126m in the area formula to get the area A2 of outer circle as:A2=π(126)²

⇒A2=22/7×126×126

×126×126⇒A2=49896

So, we get the area of the outer circle as 49896 metre square.

So, we get the area of the outer circle as 49896 metre square.Now, we need to calculate the area between the two circles which is given by the difference of A2and A1as:

So, we get the area of the outer circle as 49896 metre square.Now, we need to calculate the area between the two circles which is given by the difference of A2and A1as:A2−A1=49896−39424

So, we get the area of the outer circle as 49896 metre square.Now, we need to calculate the area between the two circles which is given by the difference of A2and A1as:A2−A1=49896−39424⇒A2−A1=10472

So, we get the surface area of the road as 10472 meter square.

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