Question

find the radius pf cone formed by the quadrant
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Answer 1

Area of a quadrant, A= (πr2)/4.

I hope this helps you.

Answer 2

Step-by-step explanation:

The formula for the volume of a cone is V = π r2 h/3

In this case we need to find the radius of the circle at the top of the cone as well as the height of the cone.

We know that the radius of the original circle from which the cone was taken was 7. Therefore the circumference of the original circle was C=2πr or 14π

Since the cone was taken from one quadrant of the circle, or 1/4 of the circle, the circumference of the circle at the top of the cone is (14/4)π = (7/2)π

Using the circumference formula again, we can determine the radius of this circle

(7/2)π = 2πr

so r = 7/4

To determine the height of the cone, we use the radius we just calculated and the fact that the original radius was 7.

The original radius becomes the slant of the cone.

What we have is a right triangle with a base of 7/4 (the radius of the circle of the cone) and a hypotenuse of 7 (slant). We can solve for the height of the cone using a2 + b2 = c2, where a = 7/4 and c = 7

(7/4)2 + b2 = 72

and b2 = 49 - 49/16 = 735/16

and b = √(735/16) = (7/4)√15 Height

Using the original formula V = π r2 h/3

V = π (7/4)2 [(7/4)√(15)] / 3

V = π (7/4)3 √15 / 3

V = (343/192) √15 π

V = 6.92π or 21.73

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