The cross section and bottom view of a flowerpot are shown above. If

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

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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

Volume of the vase = \(π(\frac{3}{2})^2*1\) + \(π(2)^2*1\)+ \(π(\frac{5}{2})^2*1\)

Or, Volume of the vase = \(\frac{9π}{4}\) + \(4π\)+ \(\frac{25π}{4}\)

Or, Volume of the vase = \(2.25π + 4π+ 6.25π\)

Or, Volume of the vase = \(12.5π\)

Hence, 12.5π*16 = 200π is the approximate amount of water that the flowervase contains.... , Answer must be (D)
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Sorry, i am lost not this - how can we infer that height is 1inch?

Each Cross-Section is a Prism with a Circular Base that raises up to a Height of 1 inch.

Rule: the Volume of Any Symmetrical Prism = (Area of Base) * (Height)

the Area of each Base is given by the Area of a Circle Formula. Base 1 has radius = 3/2. Base 2 has radius = 2. Base 3 has radius = (5/2)

and the Height = 1 inch for each Prism

the Volume (in cubic inches) that the ENTIRE Pot will hold will be equal to =

[ (pi)*(3/2)^2 * (1) ] + [ (pi) * (2)^2 * 1 ] + [ (pi) * (5/2)^2 * 1 ] =

50(pi) / 4 -----> Volume measured in Cubic Inches

The Questions asks: how many GRAMS does the Pot hold?

We are given the conversion ratio: 16 grams = 1 cubic inch

(50pi/4) cubic inches * (16 grams / 1 cubic inch) = 200(pi) grams

-D-

To determine how many grams of water the pot holds, we need to determine the volume of the pot.

We can pretend we have 3 separate cylinders:

Volume of cylinder 1 = \(πr^2h\)

Volume of cylinder 2 = \(π2.5^2h\)

Volume of cylinder 3 = \(π2^2h\)

Volume of cylinder = \(π1.5^2h\)

Adding the 3 cylinders up, we get \(6.25π + 4π + 2.25π = 12.5π\)

\(12.5π * 16 = 200π\)

Answer is D.
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