A circular rim 28 inches in diameter rotates the same number

BTGmoderatorDC wrote:A circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?

A. \(\frac{48\pi}{x}\)

B. \(75x\)

C. \(48x\)

D. \(24x\)

E. \(\frac{x}{75}\)

OA C

Source: Official Guide

We know that 1 revolution of a circle = circumference of that circle.

One revolution of a circle having a diameter of 28 inches = πd = 28π inches. Hence, x revolutions per second = 28π*x inches per second = 60∗28πx inches per minute

Given that 60∗28πx = 35πn => n = (60∗28πx) / 35π = 48x.

The correct answer: C

Hope this helps!

-Jay
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BTGmoderatorDC wrote: ↑

Mon Dec 23, 2019 7:10 pm

A circular rim 28 inches in diameter rotates the same number of inches per second as a circular rim 35 inches in diameter. If the smaller rim makes x revolutions per second, how many revolutions per minute does the larger rim makes in terms of x ?

A. \(\frac{48\pi}{x}\)

B. \(75x\)

C. \(48x\)

D. \(24x\)

E. \(\frac{x}{75}\)

OA C

Source: Official Guide

The smaller rim rotates at a rate of 28πx inches per second. Since the larger rim rotates the same number of inches per second, it rotates at a rate of 28πx inches per second also, and, in one minute, it rotates 28πx * 60 inches.

Since 1 rotation of the larger rim = its circumference = 35π, the number of rotations made by the larger rim will thus be:

(28πx * 60)/35π

(4x * 60)/ 5

4x * 12

48x

Answer: C