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03 Sep 2018, 06:06
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
55% (02:28) correct
45%
(03:11)
wrong
based on 42
sessions
History
Date
Time
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Not Attempted Yet
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. \(288 + 96\pi\)
A. \(216 + 96\pi\)
B. \(216 + 48\pi\)
C. \(216 + 36\pi\)
D. \(288 + 48\pi\)
E. \(288 + 96\pi\)
03 Sep 2018, 06:06
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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 \(96\pi + 216\).
Answer: A
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 \(96\pi + 216\).
Answer: A
firas92
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Joined: 16 Jan 2019
Last visit: 02 Dec 2024
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Location: India
Concentration: General Management
Schools: Tepper '23 (M$) Foster '23 (D)
GMAT 1: 740 Q50 V40
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22 Aug 2019, 11:19
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Bunuel
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.
Please explain
