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The radius of the front wheels of a cart is half the radius of its rear wheels. If the front wheels have a circumference of 1 meter, and the cart has traveled a distance of 1 kilometer, what is the number of revolutions made by each rear wheel?
- a)250/π
- b)500/π
- c)250
- d)500
- e)750
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The radius of the front wheels of a cart is half the radius of its rea...
Given that the front wheels have a circumference of 1 meter, we can deduce that their radius is half of this circumference, which is 1/2 meter or 0.5 meters.
Let's denote the radius of the rear wheels as R. According to the problem, the radius of the front wheels is half the radius of the rear wheels. Therefore, we can express the radius of the front wheels in terms of R as follows:
Front wheel radius = 0.5R
We know that the circumference of a circle is given by the formula C = 2πr, where C represents the circumference and r represents the radius. Using this formula, we can express the circumference of the front wheels as:
1 meter = 2π(0.5R) 1 = πR R = 1/π
Now we have the radius of the rear wheels, which is 1/π meters.
To calculate the number of revolutions made by each rear wheel, we can use the formula:
Number of revolutions = Distance traveled / Circumference of the wheel
The distance traveled is given as 1 kilometer, which is equal to 1000 meters. The circumference of a wheel is given by the formula C = 2πr.
Number of revolutions made by each rear wheel = 1000 meters / (2π(1/π)) = 1000 meters / (2π/π) = 1000 meters / 2 = 500 revolutions
Therefore, each rear wheel would make 500 revolutions.
Most Upvoted Answer
The radius of the front wheels of a cart is half the radius of its rea...
Let's call the radius of the front wheels r. Therefore, the radius of the rear wheels is 2r.
The circumference of a circle is given by the formula C = 2πr.
We are given that the front wheels have a circumference of 1 meter, so 1 = 2πr.
Solving for r, we find r = 1/(2π).
The rear wheels have a circumference of 2π(2r) = 4πr = 4π(1/(2π)) = 2 meters.
Since the cart has traveled a distance of 1 kilometer, or 1000 meters, and each rear wheel travels a distance equal to its circumference in one revolution, the number of revolutions made by each rear wheel is 1000/2 = 500.
Therefore, the number of revolutions made by each rear wheel is 500. Answer: \boxed{500}.
The circumference of a circle is given by the formula C = 2πr.
We are given that the front wheels have a circumference of 1 meter, so 1 = 2πr.
Solving for r, we find r = 1/(2π).
The rear wheels have a circumference of 2π(2r) = 4πr = 4π(1/(2π)) = 2 meters.
Since the cart has traveled a distance of 1 kilometer, or 1000 meters, and each rear wheel travels a distance equal to its circumference in one revolution, the number of revolutions made by each rear wheel is 1000/2 = 500.
Therefore, the number of revolutions made by each rear wheel is 500. Answer: \boxed{500}.
Community Answer
The radius of the front wheels of a cart is half the radius of its rea...
Given that the front wheels have a circumference of 1 meter, we can deduce that their radius is half of this circumference, which is 1/2 meter or 0.5 meters.
Let's denote the radius of the rear wheels as R. According to the problem, the radius of the front wheels is half the radius of the rear wheels. Therefore, we can express the radius of the front wheels in terms of R as follows:
Front wheel radius = 0.5R
We know that the circumference of a circle is given by the formula C = 2πr, where C represents the circumference and r represents the radius. Using this formula, we can express the circumference of the front wheels as:
1 meter = 2π(0.5R) 1 = πR R = 1/π
Now we have the radius of the rear wheels, which is 1/π meters.
To calculate the number of revolutions made by each rear wheel, we can use the formula:
Number of revolutions = Distance traveled / Circumference of the wheel
The distance traveled is given as 1 kilometer, which is equal to 1000 meters. The circumference of a wheel is given by the formula C = 2πr.
Number of revolutions made by each rear wheel = 1000 meters / (2π(1/π)) = 1000 meters / (2π/π) = 1000 meters / 2 = 500 revolutions
Therefore, each rear wheel would make 500 revolutions.
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The radius of the front wheels of a cart is half the radius of its rear wheels. If the front wheels have a circumference of 1 meter, and the cart has traveled a distance of 1 kilometer, what is the number of revolutions made by each rear wheel?a)250/πb)500/πc)250d)500e)750Correct answer is option 'D'. Can you explain this answer?
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The radius of the front wheels of a cart is half the radius of its rear wheels. If the front wheels have a circumference of 1 meter, and the cart has traveled a distance of 1 kilometer, what is the number of revolutions made by each rear wheel?a)250/πb)500/πc)250d)500e)750Correct answer is option 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about The radius of the front wheels of a cart is half the radius of its rear wheels. If the front wheels have a circumference of 1 meter, and the cart has traveled a distance of 1 kilometer, what is the number of revolutions made by each rear wheel?a)250/πb)500/πc)250d)500e)750Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The radius of the front wheels of a cart is half the radius of its rear wheels. If the front wheels have a circumference of 1 meter, and the cart has traveled a distance of 1 kilometer, what is the number of revolutions made by each rear wheel?a)250/πb)500/πc)250d)500e)750Correct answer is option 'D'. Can you explain this answer?.
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