Question below

Question

1) A barrel in the shape of a cylinder is cut half lengthwise to make a water tough for horses. Does the expression:

*3.14(1/2r)squared

represent the volume of water that the water trough holds? Explain why or why not?

*the "squared" in the equation is an exponent above the parenthesis. Thanks!

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2) The barrel in problem one is five feet long and the radius of its base is 1.5 feet. How much water will the water trough hold? Use 3.14 for pi, and round to the nearest whole cubic foot


THANKS FOR ANSWERING! :D

Answer 1

1. the formula for the volume of a cylinder (barrel) is pi • h • r²

if we cut the barrel length-wise, each half will have a volume of (pi • h • r²)/2

 

so the expression pi • 1/2r² is incorrect for two reasons, 1. no height is shown, and 2. 1/2r² does not equal r²/2

 

2. given that h = 5' and r = 1.5'

then the volume of each half will be (3.14 • 1.5'² • 5')/2  ≅  17.7f³