A wheel has a radius of 22.4 cm. What distance does it cover in 500 revolutions
Show answer Hide answer
Answer: B. 704 m
Explanation
Calculating the circumference of the wheel using its radius yields one hundred forty point eight centimeters. Multiplying the single-revolution circumference by five hundred total revolutions gives the total linear distance. Converting the total distance from centimeters to meters by dividing by one hundred yields seven hundred four meters. The circumference of a circular wheel equals two multiplied by pi and multiplied by its radius. Total rolling distance equals the wheel circumference multiplied by the total number of complete revolutions made. Unit conversions require dividing centimeters by one hundred to obtain standard metric measurements in meters.
Odometers calculate vehicle travel distances by counting wheel rotations and multiplying by tire circumference measurements. Civil engineers measure road lengths using calibrated measuring wheels in construction surveying applications. Mechanical engineers design conveyor belt systems by calculating drum rotation distances and linear belt speeds. Option A suggests two hundred fifty-two meters which underestimates the calculated distance from revolution counts. Option C suggests three hundred fifty-two meters which is exactly half of the correct total distance calculated. Option D suggests eight hundred eight meters which represents an arithmetic calculation error in circumference.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
Related questions
Q1. A circular cylinder and a sphere share the same radius and equal volumes. What is the cylinder's height________?
Show answer Hide answer
Answer: A. 4/3 times its radius
Equating the algebraic volume formula of a cylinder to that of a sphere establishes a direct dimensional relationship. Canceling common terms like pi and radius squared from both sides simplifies the volume equation sign...
Q2. A cylinder has a 2r radius and a 3r height. Find its curved surface area.
Show answer Hide answer
Answer: C. 12 πr2 sq units
The curved surface area formula requires multiplying two by pi, the radius, and the height. Substituting the given dimensions into the formula yields two multiplied by pi by two r by three r. Multiplying these numerical...
Q3. The current mean age of a married pair and their daughter is 35 years. Fifteen years ahead, the mother's age will match the combined current ages of the father and daughter. Determine the mother's current age.
Show answer Hide answer
Answer: D. 45 years
Setting up simultaneous linear equations for the family ages reflects the current mean of thirty five years. Accounting for the fifteen year future age shift matches the mother's age to the combined current ages. Solving...
Q4. Two cubes have volumes in a 729 : 1331 ratio. What is the ratio of their total surface areas?
Show answer Hide answer
Answer: A. 81 : 121
Taking the cube root of the given volume ratio of seven hundred twenty-nine to thirteen thirty-one gives the side length ratio. The cube roots of seven hundred twenty-nine and thirteen thirty-one are nine and eleven resp...
Q5. What is the volume ratio of a cube to the sphere fitted perfectly inside it________?
Show answer Hide answer
Answer: D. 6: π
The volume of a cube with side length a is determined by cubing the side dimension value. A sphere fitted perfectly inside has a radius equal to half of the cube side length. Dividing the cube volume by the sphere volume...
Q6. What are the roots of the quadratic equation 3x2 – 12x + 10 = 0?
Show answer Hide answer
Answer: D. irrational and unequal
Calculating the discriminant for three x squared minus twelve x plus ten equals fourteen minus one twenty. The resulting discriminant value of twenty four is positive but fails to form a perfect square. Quadratic equatio...