Help! Secondary 2 Math question
-
The mass of a cylinder varies directly to the product of the square of its diameter and heights. Two cylinders have their diameters in the ratio 5:4. Find the ratio of their heights if the mass of the first cylinder is 5 times that of the second cylinder.
I found 2 answers
(1) 5:16
(2) 1:4
Which i don't think is correct. Anyone have any idea how to solve?
-
Originally posted by ProjectsMates:
The mass of a cylinder varies directly to the product of the square of its diameter and heights. Two cylinders have their diameters in the ratio 5:4. Find the ratio of their heights if the mass of the first cylinder is 5 times that of the second cylinder.
I found 2 answers
(1) 5:16
(2) 1:4
Which i don't think is correct. Anyone have any idea how to solve?
What answer do you want leh ?
The ratio of the heights can be 2 : 1, sqrt 2 : 1, ..........
This question can have many answers leh.
It all depends on what you choose for the values of k1 and k2 lor ie h1 / h2 = sqrt [ 16k2 / 5k1 ]
Dont think this is a Sec 2 maths question.
It is more like a PSLE maths question that makes the P6 students find the answers by the guess and check method.
-
I agree with Seowlah. There is no unique answer as there is insufficient information given. ProjectsMates, did you leave out any important information? Otherwise, can you share with us your workings and why you don't think the answers you found are correct? Thanks!
-
Hi All:
Thanks for all the insight and assistance. I managed to get the correct answer reflected in the asisgnment book which i bought for my student.
Here is the book explanation:
http://i49.tinypic.com/2912e0l.jpg
My Method to teach my student:
Let M1 be mass of big cylinder, M2 be mass of small cylinder.
Let d1 be diameter of big cylinder, d2 be diameter of small cylinder.
Let h1 be height of big cylinder, h2 be height of small cylinder.
K is the constant.
Equations:
M1 = K x d1 x d1 x h1
M2 = K x d2 x d2 x h2
Notice "K" is the constant; i.e. same value in both equations.
Make "K" the subject for both equations
K = M1/(d1 x d1 x h1)
K = M2/(d2 x d2 x h2)
Sub in the value of M1 = 5, M2 = 1, d1 = 5, d2 = 4 [M1 is 5 because the mass of the big cylinder is said to be 5 times that of the smaller cylinder]
K = 5/25h1 = 1/5h1 (lowest term)
K = 1/16h2
Hence, 1/5h1 = 1/16h2
Last step is to find value of h1 and h2,
- 1/5h1 = 1/16h2
- 5h1 = 16h2
- 5 x (h1 = 16) = 16 x (h2 = 5); in this way, it is equalized. Hence, h1(Large cylinder): h2 (small cylinder) is = 16:5
-
Originally posted by ProjectsMates:
Hi All:
Thanks for all the insight and assistance. I managed to get the correct answer reflected in the asisgnment book which i bought for my student.
Here is the book explanation:
http://i49.tinypic.com/2912e0l.jpg
My Method to teach my student:
Let M1 be mass of big cylinder, M2 be mass of small cylinder.
Let d1 be diameter of big cylinder, d2 be diameter of small cylinder.
Let h1 be height of big cylinder, h2 be height of small cylinder.
K is the constant.
Equations:
M1 = K x d1 x d1 x h1
M2 = K x d2 x d2 x h2
Notice "K" is the constant; i.e. same value in both equations.
Make "K" the subject for both equations
K = M1/(d1 x d1 x h1)
K = M2/(d2 x d2 x h2)
Sub in the value of M1 = 5, M2 = 1, d1 = 5, d2 = 4 [M1 is 5 because the mass of the big cylinder is said to be 5 times that of the smaller cylinder]
K = 5/25h1 = 1/5h1 (lowest term)
K = 1/16h2
Hence, 1/5h1 = 1/16h2
Last step is to find value of h1 and h2,
- 1/5h1 = 1/16h2
- 5h1 = 16h2
- 5 x (h1 = 16) = 16 x (h2 = 5); in this way, it is
equalized. Hence, h1(Large cylinder): h2 (small cylinder) is =
16:5
So, projectsmates, you are a tutor ?
So, at first, you don't know how to get the answer after looking at the solution from the book and you come here to seek help from the forumers huh
Then, you got some ideas and managed to solve the question.
So, you must share your tuition fee with us leh
-
The question was a bit incomplete in the sense that they didn't mention that the mass of the cylinder varies directly to the product of the square of its diameter and heights for both cylinders, ie the constant K is the same for both cylinders. That is why Seowlah and I couldn't solve it and give you a unique answer at first.
-
Hi MUFC,
The solution given by projects mates is still only one of the many possible solutions ie
M1 = k1 x (d1)^2 x h1
M2 = k2 x (d2)^2 x h2
Given that M1 = 5M2 , d1 = (5/4) d2
M1 = 5M2
k1 x (d1)^2 x h1 = 5 k2 x (d2)^2 x h2
Substitute d1 = (5/4) d2 into
k1 x [ (5/4) d2)]^2 x h1 = 5 k2 x (d2)^2 x h2
k1h1 = (16/5) k2 h2
H1/h2 = 16k2 / 5k1.
If k2 = 1, k1 =1 or k2 = k1, then h1/h2 = 16 / 5 ie the solution given by project mates.
BUT if k2 = 5, k1 = 4, then h1/h2 = 4 / 1 ( M1=4(5)^2(4)=400, M2=5(4)^2(1)=80 )
If k2 = 5, k1 = 3, then h1/h2 = 16 / 3 ( M1=3(5)^2(16)=1200, M2=5(4)^2(3)=240 )
If k2 = ...., k1 = ......, then h1/h2 = ........, M1 = 5M2
So, as I had said in my earlier post, it all depends on what values you choose for k1 and k2 ie h1/h2 = 16k2 / 5k1 and there are many possible answers for h1/h2 for this question.
-
Yup, I agree with your answer. What I have a problem with is that the question didn't tell us that k1=k2, which would have led us to projectmates' answer. The question should be defined more clearly.
