Question 74283:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A container must hold 400 cubic inches of sand. Accurately sketch and label the dimensions of a rectangular prism, shere,and cylinder which will each hold 400 cubic inches of sand with the least amount of wasted space. Show the calculation that verifty that each container will hold 400 cubic inches.
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Use the formulas:
Prism: lwh=400 cu in
Let l=8;w=5;h=10
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Sphere: (4/3)(pi)r^3=400 cu in
r^3 = (3/4)(400)(pi)= 300pi
Take the cube root to get:
r=9.804 inches
diameter = 2r=19.61 in
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Cylinder: (pi)r^2h=400 cu in
r^2=400/(pi)h
Let h=10 then r^2 = 40/(pi)
Take the square root of 40/(pi) to get:
r= 3.56 inches
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Cheers,
Stan H.
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