Two similar cylinders have radii of 7 and 1, respectively. What is the ratio of their volumes? Two similar cylinders have radii
of 7 and 1, respectively. What is the ratio of their volumes? B. 343:1 D. 112:1
2 answers:
When can we say that two objects are similar? It's when they coincide with at least one dimension. For this case, imagine two concentric cylinders as shown in the attached figure. Both of the figures are similar. The left side coincide with their heights and base circles, while the right side only coincide in the bases of the circles. Since the heights are not specified, let's suppose the heights are equal, denoted as h.
The volume of the cylinder is equal to: V = πr²h. If you want to find the bigger volume to the smaller volume, all you have to do is divide them. Therefore, the ratio is
Ratio = π(7)²h/π(1)²h
Cancel out like terms: π and h. It leaves us with 7² and 1². So, the final answer would be
Ratio = 49
However, the answer is not given in the choices. Therefore, the heights of the cylinders are not equal. There is no way for us to know the exact ratio without the dimensions of the heights. What we can do here is apply reverse engineering. Let's conform the answer to our solution. Suppose the answer is 112:1.
Ratio: 7²*h₂/1²*h₁ = 112
That means h₂/h₁ = 2.285714286
Suppose the answer is 343:1,
Ratio: 7²*h₂/1²*h₁ = 343
That means h₂/h₁ = 7
So, I think the answer is 343:1, because the ratio's of the heights is an exact whole number. This is logical because the dimensions of the heights are also whole numbers.
The volume of the cylinder is equal to: V = πr²h. If you want to find the bigger volume to the smaller volume, all you have to do is divide them. Therefore, the ratio is
Ratio = π(7)²h/π(1)²h
Cancel out like terms: π and h. It leaves us with 7² and 1². So, the final answer would be
Ratio = 49
However, the answer is not given in the choices. Therefore, the heights of the cylinders are not equal. There is no way for us to know the exact ratio without the dimensions of the heights. What we can do here is apply reverse engineering. Let's conform the answer to our solution. Suppose the answer is 112:1.
Ratio: 7²*h₂/1²*h₁ = 112
That means h₂/h₁ = 2.285714286
Suppose the answer is 343:1,
Ratio: 7²*h₂/1²*h₁ = 343
That means h₂/h₁ = 7
So, I think the answer is 343:1, because the ratio's of the heights is an exact whole number. This is logical because the dimensions of the heights are also whole numbers.
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Step-by-step explanation:
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First, find two "exact" points!
I am going to use (0, 1) and (2, 2)
We then go to our first point, (0, 1), and count how many points up it is until we are on the same x-axis of our y. This is 1. We then do the same thing for the y-axis. This is 2. It is rise over run, so the answer is
(I hope this helps, have a nice day!)