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# M70-27

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Math Expert
Joined: 02 Sep 2009
Posts: 49258

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03 Sep 2018, 06:06
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Question Stats:

67% (00:57) correct 33% (04:24) wrong based on 3 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 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. $$288 + 96\pi$$

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Math Expert
Joined: 02 Sep 2009
Posts: 49258

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03 Sep 2018, 06:06
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 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 $$96\pi + 216$$.

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Joined: 09 Jun 2018
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08 Sep 2018, 03:07
The cylinder is fine. However, I did not get the cuboid part. There is no rule which says all the sides of a cuboid should be same. I thought that it would be similar to dimensions of the cylinder, meaning, 14-8= 6 height, length= diameter= 8, and width= height of cylinder= 6. There by giving ans 288+96pi
Intern
Joined: 19 Mar 2018
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13 Sep 2018, 19:33
I think this is a high-quality question and I don't agree with the explanation. There is no reference provided to specify that all the sides of cuboid are equal.
Re M70-27 &nbs [#permalink] 13 Sep 2018, 19:33
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# M70-27

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