Surface area and surds problem

The diagram shows a solid cylinder.

The cylinder has radius 4√3 cm and height H cm.
The total surface area of the cylinder is 56π√6 cm^2.

Find the exact value of H.
Give your answer in the form a√2 + b√ where a and b are integers.
Show your working clearly.

Can anyone help? I'm really stuck on this
edit: I forgot the π sign...sorry

(edited 3 years ago)

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Reply 1

davros

Original post by halpplez

The diagram shows a solid cylinder.

The cylinder has radius 4√3 cm and height H cm.
The total surface area of the cylinder is 56√6 cm^2.

Find the exact value of H.
Give your answer in the form a√2 + b√ where a and b are integers.
Show your working clearly.

Can anyone help? I'm really stuck on this

I think you have a number missing after the second square root on the line beginning 'Give your answer...' :smile:

Take it a step at a time. What parts of the cylinder contribute to the surface area?

Reply 2

Luwei

(56*(6)^(1/2)) = pi*48*H. Rearrange to find H.

Reply 3

halpplez

Original post by davros

I think you have a number missing after the second square root on the line beginning 'Give your answer...' :smile:

Take it a step at a time. What parts of the cylinder contribute to the surface area?

Oh right, sorry :smile:

i didnt see that- thank you for pointing it out- it should be a√2 + b√3

Reply 4

halpplez

Original post by Luwei

(56*(6)^(1/2)) = pi*48*H. Rearrange to find H.

thank you

Reply 5

username4197954

What have you done so far?

As @davros said ... consider the cylinder and how you would construct an equation for the surface area using the radius and height.

Reply 6

halpplez

Original post by Bexr

What have you done so far?

As @davros said ... consider the cylinder and how you would construct an equation for the surface area using the radius and height.

I tried writing it out- so it looked something like this:
56 π√6 = 2 πrh +2 πr^2
and then tried substituting the given radius in
56 π√6 = 2 π (4√3) h + 2π12

Reply 7

halpplez

Original post by halpplez

I tried writing it out- so it looked something like this:
56 π√6 = 2 πrh +2 πr^2
and then tried substituting the given radius in
56 π√6 = 2 π (4√3) h + 2π12

and then i tried to balance out the whole thing so i took 2π12 away from 56 π√6 which gave me 355.5385192
after that i divided my answer by 2π ( so whats left is 56.5857128 = rH)
then i divided that answer by r (4√3) which gave me 8.167444129
but the question asks to give your answer in the form a√2 + b√3
so i figure I've gone horrendously wrong somewhere

Reply 8

username4197954

check your squaring of the radius

Reply 9

davros

Original post by halpplez

I tried writing it out- so it looked something like this:
56 π√6 = 2 πrh +2 πr^2
and then tried substituting the given radius in
56 π√6 = 2 π (4√3) h + 2π12

check your last term.

If

r = 4\sqrt{3}

then what is

r^2

Reply 10

username4197954

Also, look at the equation and think what you can do with pi

Reply 11

davros

Original post by halpplez

See the comments from myself and @Bexr.

Also don't try to convert anything to decimals! You want integers and square roots (surds) at the end :smile:

Reply 12

halpplez

Original post by davros

check your last term.

If

r = 4\sqrt{3}

then what is

r^2

would it be 12?

Reply 13

halpplez

Original post by Bexr

Also, look at the equation and think what you can do with pi

ohh would you divide by pi on both sides?
so 56√6 = 2 (4√3) h +24

Reply 14

davros

Original post by halpplez

would it be 12?

Not quite - remember that

(ab)^2 = a^2b^2

Reply 15

halpplez

Original post by davros

Not quite - remember that

(ab)^2 = a^2b^2

108?

Reply 16

halpplez

Original post by halpplez

108?

oh no wait 48, right?

Reply 17

davros

Original post by halpplez

108?

(4\sqrt{3})^2 = 4^2 (\sqrt{3})^2 = ...

Reply 18

davros

Original post by halpplez

oh no wait 48, right?

you got it :smile:

Now take some factors out as Bexr suggests to make the arithmetic simpler...

Reply 19

halpplez

Original post by davros

you got it :smile:

Now take some factors out as Bexr suggests to make the arithmetic simpler...

Oh, i think i got it- 56√6 = 2 (4√3) h + 48
48 + 56√6 = 2(4√3) h
24 + 28√6 = (4√3) h
-2√3 +7√2= h
Thank you so much- both of you, i really appreciate it :smile: