Question

Lost in step 3...?


2. Apply the formula of a right circular cylinder (V = r2h) to find the volume of the object.
3. Rewrite the formula using the variable x for the radius. Substitute the value of the volume found in step 2 for V and express the height of the object in terms of x plus or minus a constant.




Diameter: 3in
Height: 4.5in
Volume: ≈31.8in

Answer 1

what this is asking you to do first is to substitute r=x into the equation:\[V = \pi r^2h\]

Answer 2

that will give you V interms of x and h

Answer 3

then, in step 1 where you found the volume, use that as the value for V and use the value 4.5 for h (the height)

Answer 4

31.8=(pi)x^2(4.5) ?

Answer 5

you should then be able to rearrange the equation to get an expression for x.

Answer 6

yes - that looks correct. now rearrange it so that you have x on the left hand side. i.e. you should end up with something like:
x = ...

Answer 7

But what does it mean by in terms of x plus or minus a constant?

Answer 8

sorry - I misread the question. you are supposed to find and expression for the height (h) in terms of x.

Answer 9

so you have:\[31.8=\pi x^2h\]now rearrange this to get the height (h) on the left hand side.

Answer 10

"plus or minus a constant" usually means something like:\[h = 55x^2+12\]or:\[h=55x^2-12\]i.e. the expression for h contains \(x^2\) plus/minus some constant. but, in this case, there should be no constant to add or subtract.

Answer 11

BTW: the expressions I showed above are just /examples/ and not the actual answer.

Answer 12

31.8=(pi)x^2(h)
-h+31.8=(pi)x^2
-h=(pi)x^2-31.8
h=-(pi)-^2+31.8

Answer 13

lets take it a step at a time...

Answer 14

we have:\[31.8=\pi x^2h\]so first lets swap the left and right hand sides as we want h to appear on the left hand side. this gives:\[\pi x^2h=31.8\]make sense so far?

Answer 15

think of actual examples, e.g.:
1 + 2 = 3

therefore:
3 = 1 + 2

so swapping left and right hand sides is a legal operation.

Answer 16

ok so far?

Answer 17

please let me know if this makes sense so far or whether I need to explain more before moving on?