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Akimi4 [234]
3 years ago
14

Which of the following functions gives the radius, r(v), of a conical artifact that is 20 inches tall as a function of its volum

e, v, in cubic inches?
Mathematics
1 answer:
nalin [4]3 years ago
5 0
By calculus or elementary geometry, we know that the formula for the volume of a cone, given pi (the constant), its height h and its radius r is:
V=pi*h*r^2/3
Lets solve this relation for the radius:
3V=pi*h*r^2

\frac{3V}{pi*h} =r^2
\sqrt{\frac{3V}{pi*h}} = r
Now we have found a general formula that gives us the radius of a cone, given its volume and height. We need only substitute height (20in) and pi=3.14 to get the numerical equation: r=0.2185*\sqrt{V}
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Answer:

25.8 ft

Step-by-step explanation:

Draw a right triangle with the right angle at the foot of the tower. The interior angle of the triangle at the top is the complement of the angle of depression. 90 - 74 = 16; it measures 16°. The leg at the bottom has length x. The height of the tower is the vertical leg and is 90 ft. We are looking for x.

For the 16° angle, x is the opposite leg, and 90 ft is the adjacent leg.

tan A = opp/adj

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x = 25.8 ft

Answer: 25.8 ft

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Step-by-step explanation:

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