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stira [4]
3 years ago
14

The ropes on either side of a swing are 1.9 m long. If a child swings through a arc length of 0.9 Determine the angle (in radian

s) through which the child swings
Mathematics
1 answer:
Yuliya22 [10]3 years ago
7 0

Answer:

theta = 9/19 radians or  approximately .4737 radians

Step-by-step explanation:

The formula for arc length is

S = r theta  

where theta is in radians.  Lets put in what we know.  The radius would be 1.9 since the ropes would be the radius.

.9 = 1.9 theta

Divide by 1.9 on each side.

.9/1.9 = theta

theta = 9/19 radians

or in decimal form it is approximately  .4737 radians



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Then, you find the volume of the dome.

Here's the formula:

volume/of/a/sphere=\frac{4}{3}\pi r^{3}\\volume/of/a/dome:\\V=\frac{2}{3}\pi r^{3} \\V=volume\\r=radius

Now, you just plug in and solve.

V=(\frac{2}{3})(\pi)(r^{3})\\V=(\frac{2}{3})(3.14)(7.2^{3})\\V=(\frac{2}{3})(3.14)(373.248)\\V=(2.093)(373.248)\\V=781.208064\\rounded:\\V=781.2

Finally, you add them together, and there's your answer!

1204.6+781.2=1985.8

Hope this helped!

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