Grain is falling from a chute onto the ground, forming a conicalpile whose diameter is always three times its height. How high isthe pile (to the nearest hundredth of a foot) when it contains 1000ft^3 of grain?
Adrianna Macias
Answered question
2022-07-25
Grain is falling from a chute onto the ground, forming a conicalpile whose diameter is always three times its height. How high isthe pile (to the nearest hundredth of a foot) when it contains of grain?
Answer & Explanation
penangrl
Beginner2022-07-26Added 17 answers
You'll need the equation for the volume of a cone, which is: where h is the height of the cone,and r is the radius. We know that the volume V = 1,000 and that diameter = 3h. Now diameter also = 2 r. so 3h =2r Divide both sides by 2 to get: (3/2) h =r. Now, wherever you see an r in the volume equation,put 3/2 h there instead. And instead of the V put in 1,000
Now you can simplify by squaring the 3/2 andthe h. or Now you can solve for height h. If you multiply both sides by 3, you have Then divide by to get Now multiply both sides by 4 / 9.
Now you have to type the left side into yourcalculator, and then take the cube root of the answer, to findh.
or (424)(1/3) = h = 7.5
valtricotinevh
Beginner2022-07-27Added 3 answers
Volume of a cone is represented by You are given the final volume of so you know that. You are told that the diameter is always 3 times the height. If you think of the cone as a triangle, the base would be thediameter and if you draw a dotted line from the tip of the triangleto the middle point of the base, that would be the height. Let's just call the height x. If the height is x then thediameter must be 3x. For the equation above, you need theheight and radius, so just divide the diameter by 2. Plug allthe numbers into the equation and solve for x:
Your x should be something around 7.515 ft. Round that to the nearest hundredth to get 7.52 ft.