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.
You might be interested in
Original height = original width = x mm
1. She made an enlarged copy...
height = 2x
width = 2x
2. She cut off a rectangle...
height = 2x
width =
3.She doubled the width...
height = 2x
width =
height * width = area
Original height was 162 mm
1. She made an enlarged copy...
height = 2x
width = 2x
2. She cut off a rectangle...
height = 2x
width =
3.She doubled the width...
height = 2x
width =
height * width = area
Original height was 162 mm
Well, remember we can't take the square root of a negative
so we see that we have
so find those values that take sqrt of a negative and restrict hem from the domain
anny value greater than 1 and less than -1
so domain is from -1 to 1, including those numbers
D=[-1,1]
a. D=[-1,1] or from -1 to 1 is domain
b. for a TI-84, go to y-editor then input
for y1
c. for a TI-84, click 2nd then window (gets to tbset) scrol down to set Δx to 0.1, then cilick 2nd again then click graph (to select table) and scroll down till you see that value of y that is the biggest, that value is x=0.7
A. domain is from -1 to 1
B. use your brain or google the instructions for your calulator
C. at x=0.7
so we see that we have
so find those values that take sqrt of a negative and restrict hem from the domain
anny value greater than 1 and less than -1
so domain is from -1 to 1, including those numbers
D=[-1,1]
a. D=[-1,1] or from -1 to 1 is domain
b. for a TI-84, go to y-editor then input
c. for a TI-84, click 2nd then window (gets to tbset) scrol down to set Δx to 0.1, then cilick 2nd again then click graph (to select table) and scroll down till you see that value of y that is the biggest, that value is x=0.7
A. domain is from -1 to 1
B. use your brain or google the instructions for your calulator
C. at x=0.7