SOLUTION: Find the exact value of the volume of a can of green beans with a diameter 8 centimeters and height of 12 centimeters. Include correct units with your solution. Use "pi" in place o

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Question 461422: Find the exact value of the volume of a can of green beans with a diameter 8 centimeters and height of 12 centimeters. Include correct units with your solution. Use "pi" in place of the pi symbol.
Answer by math-vortex(648) (Show Source):
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Find the exact value of the volume of a can of green beans with a diameter 8 centimeters and height of 12 centimeters. Include correct units with your solution. Use "pi" in place of the pi symbol.
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A can of green beans has the shape of a cylinder. We want to find the volume.
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The formula for a cylinder is
[volume] = [the area of the base] times [the height of the cylinder].
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Notice that the base of a cylinder is a circle. So our formula is
[volume] = [the area of a circle] times [the height of the cylinder].
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The area of a circle is ["pi"] times [the square of the radius]
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Let's write the whole formula is symbols.
V = volume of the cylinder
r = radius of the circle
h = height of the cylinder
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So, the formula for the volume of a cylinder is
V = "pi"*(r^2)*h
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We are given the diameter of the can, but we need the radius. Recall that the radius of a circle is half the diameter, so the radius of our can is 8/2 = 4 centimeters.
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Now we can substitute 4 for r and 12 for h to find the volume. Since volume is 3-dimensional, our answer will be in cubic centimeters.
V = "pi"*(4^2)*12
V = "pi"*16*12
V = 192"pi" cubic centimeters
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Since we are asked for an exact answer, we leave the answer in terms of "pi:.
It would look like this:

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Hope this helps!
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Ms. Figgy
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