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The holding tanks are congruent in size, and both are in the shape of a cylinder that has been cut in half vertically. The bottom of the tank is a curved surface. What is the volume of both tanks if the radius of tank #1 is 15 feet and the height of tank #2 is 120 feet? You must explain your answer using words, and you must show all work and calculations to receive credit. So I know I have to use the formula for the volume of a cylinder which is \[V=\Pi r^2h\] Since it's given that the radius is 15 and the height is 120, I plugged them into the formula. \[V=\Pi (15)^2(120)\] Is this right so far?
its makes sense to me... the congruent tanks form a cylinder, radius 15 and height 120
Then I do 15^2 which is 225. Then I multiply 225 and 120 to get 2700. Then I multiply pi and 2700 to get 2700pi, or in decimal form 8482.30016469
But it says it is cut in half vertically, so do I divide by 2?
well I read the question as the tanks are congruent halves... |dw:1437263162103:dw|
But I am finding the volume of the whole cylinder first, and then dividing by 2.
I should get the same answer, right?
well the way I read it, the 2 tanks make the whole... sorry I can't help much more that that... so I'd expect that the volume is \[V = \pi \times 15^2 \times 120\]
Okay thank you
@jim_thompson5910 could you see if you could help too?
the question asks for the volume of 1 tank so you could find the volume of the whole, divide it by 2.... and say that tank has a volume = x, since tank 2 is congruent, the combined volume is V = 2x
Right. So my final answer after dividing by 2 is 4241.15008234
Then I have to round to the nearest whole number
Wait nevermind I don't have to round.
so reading the question again, the 2 tanks are like feeding troughs |dw:1437263554473:dw|
I feel like i have the right answer, i just want to make sure lol :)
but then it says what is the volume of BOTH tanks
so do i even need to divide by 2?
V = pi*r^2*h V = pi*15^2*120 V = 27,000pi exact volume of the two tanks put together, to form one complete cylinder, is 27000pi
there's no need to divide by 2. Imagine gluing them together to form one cylinder
so my answer would be 8482.30016469
wait no hang on
I was doing 2700 not 27000
yeah you were missing a 0
Thank you :)