Two spheres are used in a certain machine. One has a volume of 7 cm3 and the other has a volume of 189 cm3. The radius of the small sphere is what fraction of the radius of the large sphere?
Which of the following represents the first step to solve this problem?
Question options:
189 ÷ 7
73
189√3
189 ÷ 3
jeff you shouldn't as questions when doing tests in spirit of math...
I recall doing this question, but can't find it
I also recall that none of the choices are correct
Can you find the "time stamp" of the post, so I can look at it again?
Yesterday at 6:17
mmmh
https://www.jiskha.com/questions/1825626/two-spheres-are-used-in-a-certain-machine-one-has-a-volume-of-7-cm3-and-the-other-has-a
did you not look at my last reply.
I cannot make it any clearer.
After my initial solution, I gave you this:
------------
Did you not look at my solution?
you could do it the long way .....
(4/3)π r1^3 = 189
r2^3 = 189(3/4)(1/π) = 567/4π
r2 = (567/4π)^(1/3) = 3.56006...
similarly
(4/3)π r2^3 = 7
r1 = ...
= 1.186687...
r2/r1 = 3.560063... / 1.186687.. = 3/1
so the smaller radius is 1/3 the larger
Why were you switching names ?????
Can you tell me the very first thing that you did to solve the solution?
I had given you two solutions:
The first one simply applied the relationship between volumes of similar objects and their corresponding dimensions.
that would be V1/V2 = r1^3/r2^3
and you would be done in 3 lines.
the second one I copied in bold font and ....
knowing that Volume of a sphere = (4/3)π r^3
just look at it
My teacher says it's one of the answers. Do you know any other possible methods? I am really struggling.
"The radius of the small sphere is what fraction of the radius of the large sphere?"
answer: the radius of the smaller is 1/3 of the radius of the larger.
proof:
larger sphere: (4/3)π r2^3 = 189
r2^3 = 189(3/4)(1/π) = 567/4π
r2 = (567/4π)^(1/3) = 3.56006...
similarly
smaller sphere: (4/3)π r1^3 = 7
r1 = ...
= 1.186687...
larger radius : smaller radius
= r2 : r1 = 3.560063... : 1.186687.. = 3 : 1
so the smaller radius is 1/3 the larger
Your are welcome to print out the last part of this solution and show it to your teacher.
None of your choices match that.
Answer choices are incorrect, end of discussion.
btw, just noticed that "Kenny" had the same solution to the same question
https://www.jiskha.com/questions/1824793/two-spheres-are-used-in-a-certain-machine-one-has-a-volume-of-7-cm3-and-the-other-has-a
To solve this problem, we need to compare the volumes of the two spheres and find the ratio of their radii. The volume of a sphere is given by the formula V = (4/3)πr³, where V is the volume and r is the radius.
The first step is to find the ratio of the volumes of the two spheres by using the formula for the volume of a sphere. However, we are not given the radius of either sphere directly. Instead, we are given the volumes of the spheres.
So, the first step is to find the ratio of the volumes of the two spheres. This can be done by dividing the volume of the larger sphere by the volume of the smaller sphere.
Therefore, the correct first step to solve this problem is: 189 ÷ 7.