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

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Re: The cross section and bottom view of a flowerpot are shown above. If [#permalink]
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Bunuel wrote:

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

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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Re: The cross section and bottom view of a flowerpot are shown above. If [#permalink]
Sorry, i am lost not this - how can we infer that height is 1inch?
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The cross section and bottom view of a flowerpot are shown above. If [#permalink]
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-
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Re: The cross section and bottom view of a flowerpot are shown above. If [#permalink]
Bunuel wrote:

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

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 $$6.25π + 4π + 2.25π = 12.5π$$

$$12.5π * 16 = 200π$$

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Re: The cross section and bottom view of a flowerpot are shown above. If [#permalink]
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Re: The cross section and bottom view of a flowerpot are shown above. If [#permalink]
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