A container must hold 400 cubeic inches of sand. Accurately sketch and label the dimensions of a rectangular prism, sphere, and cylinder which will each hold the 400 cubic inches of sand with the least amount of wasted space. Show the calculations that verify that each container will hold 400 cubic inches.
Show each step of your work && if you can state the mathematical reason/s why you chose each of your steps.
2006-09-21 09:03:59 · 4 answers · asked by Anonymous in Education & Reference ➔ Teaching
volume of a rectangular prism or cylinder: area of base x height
volume of a sphere 4/3{pi}r^3 (or 4/3 x pi x r to the third power)
you can figure it out from there.
2006-09-21 09:13:05 · answer #1 · answered by John J 6 · 0⤊ 0⤋
You need the formulas for calculating the volume of those different shapes:
Volume of a rectangular prism= length x width x hight
Volume of a cylinder=Pi x r(squared) x hight
The radius r is half the diameter
Volume of a sphere = 4/3 Pi x r(cubed)
Pi = approx 3.14
Just set the formula for the sphere equal to 400 and you can easily get that radius for the sphere.
Next try and sketch a cylinder shape as close as you can around the sphere you've drawn to come up with a cylinder that will hold as close to 400 cubic inches as you can.
Imagine your sphere just fitting inside a cylinder. The cross section of the cylider would have the same radius as the sphere wouldn't it?
Then think about the rectangular prism. It would have a cross sectional width which was just the right size to fit the sphere inside. Your rectangular prism is just a distorted cube so work out the dimensions of a cube which will hold the sphere (easy because it's width, length and hight would be equal to twice the radius of the sphere) and distort it to convert it into a rectangular prism. Use trial and error to morph your cube to give dimensions for a rectangular prism that will have a volume of just above 400.
That's how I'd tackle this problem. Maybe somebody can give you a better way.
2006-09-21 10:08:12 · answer #2 · answered by Anonymous · 0⤊ 0⤋
Is this helping with math homework, I'm still trying to pass College Algebra and I am a College Senior!
2006-09-21 09:05:12 · answer #3 · answered by boykin0308 2 · 0⤊ 0⤋
18 to 26 to commence with........ that's 40 4 people then you somewhat've an entire form of 88 people yet you may keep the comparable ratio so........... 18x2=36 26x2=fifty two 36+fifty two=88 and...... 36/fifty two=18/26............. so 36 is the respond
2016-12-12 12:30:03 · answer #4 · answered by ? 4 · 0⤊ 0⤋