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# M70-27

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Math Expert
Joined: 02 Sep 2009
Posts: 64101

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03 Sep 2018, 05:06
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Difficulty:

45% (medium)

Question Stats:

67% (02:28) correct 33% (03:10) wrong based on 18 sessions

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The snack company Incredible Edible built a 14-meter-high statue in the shape of a lowercase “i” and filled it with peanut butter. If the dot at the top of the “i” is a cylinder with a diameter of 8 meters and a height of 6 meters, which is tangent to the cube that makes up the bottom of the “i”, how much peanut butter was needed to fill the statue?

A. $$216 + 96\pi$$
B. $$216 + 48\pi$$
C. $$216 + 36\pi$$
D. $$288 + 48\pi$$
E. $$288 + 96\pi$$

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Math Expert
Joined: 02 Sep 2009
Posts: 64101

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03 Sep 2018, 05:06
Official Solution:

The snack company Incredible Edible built a 14-meter-high statue in the shape of a lowercase “i” and filled it with peanut butter. If the dot at the top of the “i” is a cylinder with a diameter of 8 meters and a height of 6 meters, which is tangent to the cube that makes up the bottom of the “i”, how much peanut butter was needed to fill the statue?

A. $$216 + 96\pi$$
B. $$216 + 48\pi$$
C. $$216 + 36\pi$$
D. $$288 + 48\pi$$
E. $$288 + 96\pi$$

We’ll go for PRECISE because all the numbers we need are in the question.

This question asks us about the volume of the statue, which is actually the sum of the volumes of separate shapes: a cylinder and a cube. Let’s start with the cylinder: it has a diameter of 8 meters, meaning its radius is 4 meters – so its volume is $$\pi r^2h = \pi 4^2*6 = 96\pi$$. Now let’s look at the cube: its height is the height of the statue minus the diameter of the dot = $$14 – 8 = 6$$. Since all its dimensions are the same, the volume of the cube is $$a^3 = 6^3 = 216$$. So the total volume of the dot is $$96\pi + 216$$.

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Director
Joined: 16 Jan 2019
Posts: 597
Location: India
Concentration: General Management
WE: Sales (Other)

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22 Aug 2019, 10:19
2
Bunuel wrote:
Official Solution:

The snack company Incredible Edible built a 14-meter-high statue in the shape of a lowercase “i” and filled it with peanut butter. If the dot at the top of the “i” is a cylinder with a diameter of 8 meters and a height of 6 meters, which is tangent to the cuboid that makes up the bottom of the “i”, how much peanut butter was needed to fill the statue?

A. $$216 + 96\pi$$
B. $$216 + 48\pi$$
C. $$216 + 36\pi$$
D. $$288 + 48\pi$$
E. $$288 + 96\pi$$

We’ll go for PRECISE because all the numbers we need are in the question.

This question asks us about the volume of the statue, which is actually the sum of the volumes of separate shapes: a cylinder and a cuboid. Let’s start with the cylinder: it has a diameter of 8 meters, meaning its radius is 4 meters – so its volume is $$\pi r^2h = \pi 4^2*6 = 96\pi$$. Now let’s look at the cuboid: its height is the height of the statue minus the diameter of the dot = $$14 – 8 = 6$$. Since all its dimensions are the same, the volume of the cuboid is $$a^3 = 6^3 = 216$$. So the total volume of the dot is $$96\pi + 216$$.

Hi Bunuel,

Why are all the dimensions of the cuboid same?

If it is mentioned as cube then the dimensions are same, but here its a cuboid and I think it makes more sense that the dimensions of the cuboid must be 6X8X6 which gives us answer choice E.

Manager
Joined: 05 May 2016
Posts: 142
Location: India

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04 Oct 2019, 23:57
1
Hi Bunuel,
Why are all the dimensions same for the cuboid. Its not mentioned in the question, and the sides are same for a cube. How did you conclude that all sides are same.

Thank you.
Math Expert
Joined: 02 Sep 2009
Posts: 64101

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05 Oct 2019, 00:37
bm2201 wrote:
Hi Bunuel,
Why are all the dimensions same for the cuboid. Its not mentioned in the question, and the sides are same for a cube. How did you conclude that all sides are same.

Thank you.

Yes, it should be cube instead of cuboid. Edited. Thank you.
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Joined: 14 Feb 2014
Posts: 32

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17 Feb 2020, 08:12
Hi Bunuel,

May i ask you, why the height of the cube is equal to it's diameter, which is 8, instead of 6? it doesnot make sense to me.

The question clearly states that a cylinder with a diameter of 8 meters and a height of 6 meters. why donot you subtract the 6 from the14, which gives us a height/side lengths of 8 for the cube?
Intern
Joined: 01 May 2018
Posts: 7

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17 Apr 2020, 14:31
Rebaz wrote:
Hi Bunuel,

May i ask you, why the height of the cube is equal to it's diameter, which is 8, instead of 6? it doesnot make sense to me.

The question clearly states that a cylinder with a diameter of 8 meters and a height of 6 meters. why donot you subtract the 6 from the14, which gives us a height/side lengths of 8 for the cube?

Because the dot on the top of the cube is a lying down cylinder, so the circle is facing outside and when you look at it, it appears as a dot. Hope you get it I can't draw here.
M70-27   [#permalink] 17 Apr 2020, 14:31

# M70-27

Moderators: chetan2u, Bunuel