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09 Sep 2022, 02:30
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
51% (02:33) correct
49%
(02:01)
wrong
based on 37
sessions
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Logan is constructing a scaled model of his town. The city's water tower stands 40 meters high, and the top portion is a sphere that holds 100,000 liters of water. Logan's miniature water tower holds 0.1 liters. How tall, in meters, should Logan make his tower?
(A) 0.04
(B) \(\frac{0.4}{\pi}\)
(C) 0.4
(D) \(\frac{4}{\pi}\)
(E) 4
(A) 0.04
(B) \(\frac{0.4}{\pi}\)
(C) 0.4
(D) \(\frac{4}{\pi}\)
(E) 4
10 Sep 2022, 04:03
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This is an easy problem if one understands how similarly works.
Let us understand that by a couple of triangles.
So with a similar understanding, we can say in that question, that the ratio of the volume of actual: miniature = 100,000: 0.1 = 1,000,000: 1
So, the answer is \(\frac{40}{100}\) = 0.4
Option C.
Let us understand that by a couple of triangles.
- A triangle is having sides of 3, 4, and 5. Another similar triangle is having a side of 6, 8, and 10.
- The sides are in the ratio 1: 2 so any entity that is one-dimensional will be in the same ratio. For example, perimeter, corresponding heights, inradius, circumradius .. etc.
Anything that is two-dimensional will have a ratio squared of the side ratio and hence here it will be \(1^2: 2^2\)
So with a similar understanding, we can say in that question, that the ratio of the volume of actual: miniature = 100,000: 0.1 = 1,000,000: 1
- Since volume is a 3-D entity so we must take the cube root of it to the 1-D ratio.
We are asked about height so we can say that height must be in the ratio \(\sqrt[3]{1000000} : \sqrt[3]{1}\) = 100:1
So, the answer is \(\frac{40}{100}\) = 0.4
Option C.
11 Sep 2022, 08:23
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We can find ratio of dimension of the actual sphere to the model sphere. This ratio must be constant between the actual height and the model height.
The working is shown in the attached image.
Option C
The working is shown in the attached image.
Option C
Attachments
Screenshot 2022-09-11 205220.png [ 144.37 KiB | Viewed 1602 times ]
