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Paraphin [41]
4 years ago
8

Two gears are adjusted so that the smaller gear drives the larger one. The radius of the smaller gear is 3.7 cm and the radius o

f the larger gear is 7.1 cm.
If the smaller gear rotates through an angle of 300°, through how many degrees does the larger gear rotate?
Mathematics
1 answer:
SIZIF [17.4K]4 years ago
7 0

Answer:

\theta=156^0

Step-by-step explanation:

The smaller gear rotates through an angle of 300°.

In radian, 300°= 300X\frac{\pi}{180} =\frac{5\pi}{3}

The arc length, s on the smaller gear(with a radius of 3.7 cm) is:

s=r\theta

s= \frac{5\pi}{3} X 3.7=\frac{18.5\pi}{3}

The larger gear moves through the same arc length.

Therefore:

Arc length of the larger gear, s=\frac{18.5\pi}{3}

Radius of the larger gear =7.1cm

s=r\theta

\frac{18.5\pi}{3}=7.1\theta\\\theta=\frac{18.5\pi}{3X7.1}\\\theta=\frac{18.5\pi}{21.3}

To convert back to degrees

\theta=\frac{18.5\pi}{21.3}\\\theta=\frac{18.5\pi}{21.3}X\frac{180}{\pi} =156.33\\\\\theta=156^0

The larger gear rotates through an angle of 156 degrees.

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