Express y in terms of x help

Basically, one of my exam questions says express y in terms of x

Q) A cone has radius 2x and height y. A sphere has radius 3x

Express y in terms of x

A) I have the answer but I do not know how they got that answer, I need to learn the method involved. please. the solution is...

1/3pi(2x)^2y=4/3pi(3x)^3
4pi x^2y=4pi(3x)^3
x^y=27x^3
y=27

Please can someone show me how they worked out that method. I get the top line of working, that's simple, I become stuck on the 2nd line, how did they get 4pi????

Thanks :smile:

Reply 1

generalebriety

16

Multiply both sides by 3. Then notice that (2x)^2 = 4x^2.

Reply 2

Sophie Maywood

OP

What do you meen multiply both siides by 3

Reply 3

yodude888

16

You didn't specify - are they saying that they have equal volumes? surface areas?

Reply 4

generalebriety

16

Sophie Maywood

What do you meen multiply both siides by 3

Take the first line of working (the line you said you understood), and multiply the left-hand side and the right-hand side of that equation by 3.

Reply 5

Sophie Maywood

OP

Yes they both have equal volumes but why do you multiply by 3?

Reply 6

benwellsday

12

The have equal volume.

\frac {(2x)^2y\pi}{3} = \frac {4\pi(3x)^3}{3}

Both sides have a common denominator, 3, you can multiply it over, or multiply both sides by 3 as was already said, to cancel it out.

(2x)^2y\pi = 4\pi(3x)^3

The rest is rearranging an equation.

Reply 7

Sophie Maywood

OP

It also says give your answer in its simplest form- if that helps anyone?

Reply 8

Sophie Maywood

OP

Yes but how do you rearrange?

Reply 9

Guaglio

Sophie Maywood

Basically, one of my exam questions says express y in terms of x

Q) A cone has radius 2x and height y. A sphere has radius 3x

Express y in terms of x

A) I have the answer but I do not know how they got that answer, I need to learn the method involved. please. the solution is...

1/3pi(2x)^2y=4/3pi(3x)^3
4pi x^2y=4pi(3x)^3
x^y=27x^3
y=27

Please can someone show me how they worked out that method. I get the top line of working, that's simple, I become stuck on the 2nd line, how did they get 4pi????

Thanks :smile:

does the Q say whether the volumes of the cone and sphere are equal?

Also, y = 27 is not expressing y in terms of x

Reply 10

benwellsday

12

If you can't rearrange that then maybe you should get some teaching from proper teachers because it's not the sort of thing you would want to learn off the internet, too much chance of getting something wrong.