In cutting down a tree of radius 24 inches, a notch is made, one face of which is horizontal and the other inclined to the first at an angle of 60 degrees. if the edge of the notch passes through the center of the tree, find the volume of wood cut out in making the notch.

about 15,962.6 cubic inches

Step-by-step explanation:

The formula for the volume of a cylindrical wedge with its edge a diameter is ...

V = (2/3)h·r^2

Since the cut is at a 60° angle, the height of the opening is ...

(24 in)·tan(60°) ≈ 41.56922 in

Then the volume is ...

V = (2/3)(41.56922 in)(24 in)^2 ≈ 15,962.8 in^3

20%

step-by-step explanation:

look at the picture.

1.

ef : ab = 2 : 3

gf : cb = 2 : 3

gh : cd = 2 : 3

he : da = 2 : 3

2.

∠a ≅ ∠e

∠b ≅ ∠f

∠c ≅ ∠g

∠d ≅ ∠h

3.

use pythagorean theorem:

the length of the abcd trapezoid sides:

|ab| = 3 cm

|bc| = 10 cm

|cd| = 3(3) cm = 9 cm

|da| = 8 cm

the perimeter of abcd = 3 + 10 + 9 + 8 = 30 cm

the ratio of perimeters of the tarapezoids is equal 2 : 3.

substitute:

      cross multiply

      divide both sides by 3