Fig. 15.16 Shows The Innermost Lane Of A Running Track. At Each End Of The Rectangle Is A Semicircle. How Much Distance Would Kanika Cover In Running Once Round The Track? 56 M 112 M Fig. 15.16​
Introduction
In this article, we will explore the concept of calculating the distance around a running track. The track in question consists of a rectangle with semicircles at each end. We will use mathematical formulas to determine the total distance that a runner would cover in running once around the track.
Understanding the Track
The track is a combination of a rectangle and two semicircles. The rectangle has a length of 84 m and a width of 1.22 m. The semicircles are at each end of the rectangle, and their radii are equal to half of the width of the rectangle, which is 0.61 m.
Calculating the Distance
To calculate the total distance around the track, we need to calculate the distance around the rectangle and the distance around the two semicircles. We will then add these two distances together to get the total distance.
Distance Around the Rectangle
The distance around the rectangle is equal to its perimeter. The formula for the perimeter of a rectangle is:
P = 2(l + w)
where P is the perimeter, l is the length, and w is the width.
Substituting the values given in the problem, we get:
P = 2(84 + 1.22) P = 2(85.22) P = 170.44 m
Distance Around the Semicircles
The distance around a semicircle is equal to half of the circumference of a full circle. The formula for the circumference of a circle is:
C = 2Ï€r
where C is the circumference, π is a mathematical constant approximately equal to 3.14, and r is the radius.
Substituting the value of the radius of the semicircle, we get:
C = 2Ï€(0.61) C = 2(3.14)(0.61) C = 3.84 m
Since we want the distance around the semicircle, we need to divide the circumference by 2:
D = 3.84 / 2 D = 1.92 m
However, there are two semicircles, one at each end of the rectangle. Therefore, we need to multiply the distance around one semicircle by 2:
D_total = 2(1.92) D_total = 3.84 m
Total Distance Around the Track
The total distance around the track is equal to the distance around the rectangle plus the distance around the two semicircles:
Total Distance = P + D_total Total Distance = 170.44 + 3.84 Total Distance = 174.28 m
Conclusion
In this article, we calculated the total distance around a running track that consists of a rectangle with semicircles at each end. We used mathematical formulas to determine the distance around the rectangle and the distance around the two semicircles. We then added these two distances together to get the total distance. The total distance around the track is approximately 174.28 m.
Final Answer
Introduction
In our previous article, we explored the concept of calculating the distance around a running track. The track in question consists of a rectangle with semicircles at each end. We used mathematical formulas to determine the total distance that a runner would cover in running once around the track. In this article, we will answer some frequently asked questions related to calculating distance around a running track.
Q: What is the formula for calculating the distance around a rectangle?
A: The formula for calculating the distance around a rectangle is:
P = 2(l + w)
where P is the perimeter, l is the length, and w is the width.
Q: What is the formula for calculating the distance around a semicircle?
A: The formula for calculating the distance around a semicircle is:
D = C / 2
where D is the distance around the semicircle, C is the circumference of a full circle, and r is the radius of the semicircle.
Q: How do I calculate the circumference of a circle?
A: The formula for calculating the circumference of a circle is:
C = 2Ï€r
where C is the circumference, π is a mathematical constant approximately equal to 3.14, and r is the radius.
Q: What is the total distance around a track with a rectangle and two semicircles?
A: The total distance around a track with a rectangle and two semicircles is equal to the distance around the rectangle plus the distance around the two semicircles:
Total Distance = P + 2D
where P is the perimeter of the rectangle, and D is the distance around one semicircle.
Q: How do I calculate the distance around a track with multiple semicircles?
A: To calculate the distance around a track with multiple semicircles, you need to calculate the distance around each semicircle and add them together. The formula for calculating the distance around a semicircle is:
D = C / 2
where D is the distance around the semicircle, C is the circumference of a full circle, and r is the radius of the semicircle.
Q: What is the significance of the radius of a semicircle in calculating distance?
A: The radius of a semicircle is an important factor in calculating distance around a track with semicircles. The radius determines the circumference of the semicircle, which in turn determines the distance around the semicircle.
Q: Can I use a calculator to calculate the distance around a track?
A: Yes, you can use a calculator to calculate the distance around a track. However, it's always a good idea to double-check your calculations to ensure accuracy.
Conclusion
In this article, we answered some frequently asked questions related to calculating distance around a running track. We covered topics such as the formula for calculating the distance around a rectangle, the formula for calculating the distance around a semicircle, and the significance of the radius of a semicircle in calculating distance. We hope this article has been helpful in clarifying any doubts you may have had about calculating distance around a running track.
Final Answer
The final answer is: