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22 May 2020, 07:18
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The cross section and bottom view of a flowerpot are shown above. If the pot is filled to the top with water (approximate density 16 grams per cubic inch), approximately how many grams of water does the pot hold?
A. \(100\pi\)
B. \(144\pi\)
C. \(192\pi\)
D. \(200\pi\)
E. \(400\pi\)
PS21254
Attachment:
1.png [ 4.1 KiB | Viewed 10427 times ]
yashikaaggarwal
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22 May 2020, 07:32
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Let the flower pot consist of 3 cylinder of diameter 3,4,&5 respectively.
Radius will be 1.5,2,2.5
Volume of lowest cylinder => πr^2h
=> π(1.5)^2*1
=> 2.25π ------(1)
Volume of middle cylinder => πr^2h
=> π(2)^2*1
=> 4π ------(2)
Volume of upper cylinder => πr^2h
=> π(2.5)^2*1
=> 6.25π ------(3)
Adding 1+2+3
We get,
2.25π+4π+6.25π=12.5 cubic inch -----(4)
Density is 16 grams per cubic inch
=> 16*12.5π=200π
Answer is D
Posted from my mobile device
Radius will be 1.5,2,2.5
Volume of lowest cylinder => πr^2h
=> π(1.5)^2*1
=> 2.25π ------(1)
Volume of middle cylinder => πr^2h
=> π(2)^2*1
=> 4π ------(2)
Volume of upper cylinder => πr^2h
=> π(2.5)^2*1
=> 6.25π ------(3)
Adding 1+2+3
We get,
2.25π+4π+6.25π=12.5 cubic inch -----(4)
Density is 16 grams per cubic inch
=> 16*12.5π=200π
Answer is D
Posted from my mobile device
22 May 2020, 07:38
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Bunuel
The cross section and bottom view of a flowerpot are shown above. If the pot is filled to the top with water (approximate density 16 grams per cubic inch), approximately how many grams of water does the pot hold?
A. \(100\pi\)
B. \(144\pi\)
C. \(192\pi\)
D. \(200\pi\)
E. \(400\pi\)
PS21254
Attachment:
1.png
We can treat the above shape as consisting of 3 separate cylinders
So, the volume of the flower pot = (volume of cylinder with height 1 and diameter 3) + (volume of cylinder with height 1 and diameter 4) + (volume of cylinder with height 1 and diameter 5)
= (volume of cylinder with height 1 and RADIUS 1.5) + (volume of cylinder with height 1 and RADIUS 2) + (volume of cylinder with height 1 and RADIUS 2.5)
Volume of cylinder \(= \pi r^2 h\)
So, the volume of the flower pot \(= (\pi)(1.5^2)(1)+(\pi)(2^2)(1)+(\pi)(2.5^2)(1)\)
\(= (\pi)(2.25)(1)+(\pi)(4)(1)+(\pi)(6.25)(1)\)
\(= 2.25\pi+4\pi+6.25\pi\)
\(= 12.5\pi\) cubic inches
GIVEN: approximate density 16 grams per cubic inch
So, weight of water in flower pot \(= (16)(12.5\pi) = 200\pi\)
Answer: D
Cheers,
Brent
