SOLUTION: A hole 10 cm in diameter is to be punched out from a
right circular cone (base on top) having a diameter of 16
cm and a height of 24 cm. Determine the total volume
punched ou
Algebra.Com
Question 1182676: A hole 10 cm in diameter is to be punched out from a
right circular cone (base on top) having a diameter of 16
cm and a height of 24 cm. Determine the total volume
punched out.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
The statement of the problem is deficient -- we have to know where/how the hole is drilled in the cone.
Re-post with a complete description of the problem.
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The only way to solve the problem (without really ugly math) is if we assume the hole is parallel to and centered on the axis of the cone. In that case....
In a 2-dimensional cross section of the cone sliced in half vertically, we have a right triangle with legs 8 and 24, which are the radius and height of the cone; and inscribed in that right triangle is a rectangle with width 5, the radius of the hole, and a length to be determined.
The rectangle inscribed in the triangle creates two other triangles similar to the original triangle. A similar triangle adjacent to the rectangle has short leg 8-5=3; a similar triangle below the rectangle has short leg 5.
By similar triangles, the height of the triangle with short leg 5 is 15.
Going back to 3 dimensions, the volume cut out by the hole is the sum of the volume of a right circular cone with radius 5 and height 15 and the volume of a cylinder with radius 5 and height 24-15=9.
Rounded to 2 decimal places....
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