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sleet_krkn [62]
2 years ago
9

What is the length of the arc with a measure of 200 degrees in a circle with a radius of 31 inches?

Mathematics
1 answer:
Kipish [7]2 years ago
6 0

Answer:

403π/9 or 140.67

Step-by-step explanation:

First, you have to find the circumference of the circle

Circle circumference equation:

Circumference = dπ (Circumference = diameter x pi)

You have a radius of 31 which is equal to 62 diameter (diameter is double the radius)

So:

C = 62π

Now, you need to know that a full circle is 360 degrees and we want only 200 degrees of that,

So in other words, you want 200/360 of the circle's circumference.

You can find the measure of the 200 degree arc by doing

62π x \frac{200}{360} = \frac{403pi}{9} or 140.67

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In the diagram below, angle 7 equals 61°.<br><br><br><br> What is the measure of angle 8?
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Read 2 more answers
2. The height of one square pyramid is 24 m. A similar pyramid has a height of 8 m. The volume of the larger pyramid is 648 m3.
Dmitrij [34]
Larger PyramidHeight 24 Volume 648

Pyramid Volume = (Area of the Base * Height) ÷ 3648 = Base Area * 24 / 3Base Area = 648 * 3 / 24Base Area = 648 / 8Base Area = 81Base Length = 9
a) The Scale Factor between the Small & Large PyramidLength - 3LATERAL Area - 9Volume - 27

Slant Height^2 = 4.5^2 + 24^2Slant Height^2 = <span> <span> 596.25 </span> </span> <span><span>Slant Height^2 = 24.4182308941 </span> </span>
b)
Large Pyramid Area = (½ * Perimeter of Base * Slant Height) + Base AreaLarge Pyramid Area = (.5 * 36 * <span>24.4182308941) + 81
</span>Large Pyramid Area = 439.5281560938 + 81
Large Pyramid TOTAL Area = <span> <span> 520.5281560938 </span> </span> <span>Large Pyramid LATERAL Area =<span> 439.5281560938 </span> </span>


**********************************************************************************c)
Smaller PyramidHeight 8Surface Area = 124
This pyramid has dimensions that are one third of the larger pyramid.Therefore, it has a base length of 3.Base Area = 9.
Its base perimeter would be 12.
Small Pyramid Volume = (Area of the Base * Height) ÷ 3Small Pyramid Volume = ( 9 * 8 ) / 3Small Pyramid Volume = 72 / 3
c) Small Pyramid Volume =24 cubic meters

d) Ratio of larger pyramid volume to smaller pyramid volume648 / 24 = 27The reason? Volume is a 3 dimensional quantity.  The Larger pyramid is 3 times larger in terms of the base measurement.9 meters vs 3 meters - a factor of 3When we compare volumes, we have to cube this factor.3^3 = 27

Source : http://www.1728.org/volpyrmd.htm

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