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# Maths Help Needed (Again) watch

1. My Thanks goes to anybody at all who is able to help me with this question which I am attempting at the moment

A can of orange juice is in the form of a right-circular cylinder and holds a volume of 1000 cm^3 of fluid. what dimensions of the can will give the smallest surface area?

and also Find the area between the curve y=x^3 -4x^2 + 3x (0 < x < 3) and the x-axis.

If anyone can help or guide me in the right direction I would be very thankful.

All the best

Louk
2. (Original post by Louk)
My Thanks goes to anybody at all who is able to help me with this question which I am attempting at the moment

A can of orange juice is in the form of a right-circular cylinder and holds a volume of 1000 cm^3 of fluid. what dimensions of the can will give the smallest surface area?

and also Find the area between the curve y=x^3 -4x^2 + 3x (0 < x < 3) and the x-axis.

If anyone can help or guide me in the right direction I would be very thankful.

All the best

Louk
do u know calculus? if so, then this is the best way to do it...

u know that pi * r^2 * h = 1000.
and that pi * r^2 * 2 + 2 pi * r * h is the expression for surface area.
Get the first expression in terms of h, then sub it into the second.
If you consider f(x) = the second expression, the dimensions of the can will be the values of R and H for which f(x) is a minimum (in this case, solve f'(x) = 0).
3. (Original post by Louk)
My Thanks goes to anybody at all who is able to help me with this question which I am attempting at the moment

A can of orange juice is in the form of a right-circular cylinder and holds a volume of 1000 cm^3 of fluid. what dimensions of the can will give the smallest surface area?

and also Find the area between the curve y=x^3 -4x^2 + 3x (0 < x < 3) and the x-axis.

If anyone can help or guide me in the right direction I would be very thankful.

All the best

Louk
for the second one, you just integrate y wrt x, and put in the limits

so your integrated y will be 1/4 x^4 - 4/3 x^3 + 3/2 x^2. put in x = 3, and you will get your answer.
4. thank you very much!!!!!!!

Louk

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