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Optimization of Triangular Prism Surface Area
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I am working on a math project on optimization and have a triangular prism with a given volume of 48 cubic centimeters. I am supposed to develop a function for the surface area of the equilateral triangular prism, as well as determine the dimensions that will minimize the surface area of the prism.
I attempted the question by plugging the volume into the volume formula and rearranging to find $y$, however, I am unsure of what equation to use for the surface area as I know it should be different (I think) from the normal $SA=bh+(s_1+s_2+s_3)H$.
I just spent the past couple hours trying to figure it out without much outcome. I would appreciate any help! Thank you!
optimization area volume
edited Jul 28 at 4:36
高田航
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asked Jul 28 at 3:15
John Micheal
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I am working on a math project on optimization and have a triangular prism with a given volume of 48 cubic centimeters. I am supposed to develop a function for the surface area of the equilateral triangular prism, as well as determine the dimensions that will minimize the surface area of the prism.
I attempted the question by plugging the volume into the volume formula and rearranging to find $y$, however, I am unsure of what equation to use for the surface area as I know it should be different (I think) from the normal $SA=bh+(s_1+s_2+s_3)H$.
I just spent the past couple hours trying to figure it out without much outcome. I would appreciate any help! Thank you!
optimization area volume
edited Jul 28 at 4:36
高田航
1,116318
asked Jul 28 at 3:15
John Micheal
11
You need to define the variables in your surface area equation. Given that the bases are in the same orientation (definition of prism) and they are equilateral, the sides of the prism have the same area. They are rectangles with the side of the triangle and the height as sides. You have only two variables, the side of the triangle and the height of the prism. Write the equation that computes the volume in terms of these and set it to $48$. Use that to eliminate one of the variables in the surface area equation, then differentiate, set to zero...
– Ross Millikan
Jul 28 at 4:02
add a comment |Â
up vote
-1
down vote
favorite
up vote
-1
down vote
favorite
I am working on a math project on optimization and have a triangular prism with a given volume of 48 cubic centimeters. I am supposed to develop a function for the surface area of the equilateral triangular prism, as well as determine the dimensions that will minimize the surface area of the prism.
I attempted the question by plugging the volume into the volume formula and rearranging to find $y$, however, I am unsure of what equation to use for the surface area as I know it should be different (I think) from the normal $SA=bh+(s_1+s_2+s_3)H$.
I just spent the past couple hours trying to figure it out without much outcome. I would appreciate any help! Thank you!
optimization area volume
edited Jul 28 at 4:36
高田航
1,116318
asked Jul 28 at 3:15
John Micheal
11
I am working on a math project on optimization and have a triangular prism with a given volume of 48 cubic centimeters. I am supposed to develop a function for the surface area of the equilateral triangular prism, as well as determine the dimensions that will minimize the surface area of the prism.
I attempted the question by plugging the volume into the volume formula and rearranging to find $y$, however, I am unsure of what equation to use for the surface area as I know it should be different (I think) from the normal $SA=bh+(s_1+s_2+s_3)H$.
I just spent the past couple hours trying to figure it out without much outcome. I would appreciate any help! Thank you!
optimization area volume
edited Jul 28 at 4:36
高田航
1,116318
asked Jul 28 at 3:15
John Micheal
11
edited Jul 28 at 4:36
高田航
1,116318
edited Jul 28 at 4:36
高田航
1,116318
edited Jul 28 at 4:36
高田航
1,116318
1,116318
asked Jul 28 at 3:15
John Micheal
11
asked Jul 28 at 3:15
John Micheal
11
asked Jul 28 at 3:15
John Micheal
11
11
You need to define the variables in your surface area equation. Given that the bases are in the same orientation (definition of prism) and they are equilateral, the sides of the prism have the same area. They are rectangles with the side of the triangle and the height as sides. You have only two variables, the side of the triangle and the height of the prism. Write the equation that computes the volume in terms of these and set it to $48$. Use that to eliminate one of the variables in the surface area equation, then differentiate, set to zero...
– Ross Millikan
Jul 28 at 4:02
add a comment |Â
You need to define the variables in your surface area equation. Given that the bases are in the same orientation (definition of prism) and they are equilateral, the sides of the prism have the same area. They are rectangles with the side of the triangle and the height as sides. You have only two variables, the side of the triangle and the height of the prism. Write the equation that computes the volume in terms of these and set it to $48$. Use that to eliminate one of the variables in the surface area equation, then differentiate, set to zero...
– Ross Millikan
Jul 28 at 4:02
You need to define the variables in your surface area equation. Given that the bases are in the same orientation (definition of prism) and they are equilateral, the sides of the prism have the same area. They are rectangles with the side of the triangle and the height as sides. You have only two variables, the side of the triangle and the height of the prism. Write the equation that computes the volume in terms of these and set it to $48$. Use that to eliminate one of the variables in the surface area equation, then differentiate, set to zero...
– Ross Millikan
Jul 28 at 4:02
You need to define the variables in your surface area equation. Given that the bases are in the same orientation (definition of prism) and they are equilateral, the sides of the prism have the same area. They are rectangles with the side of the triangle and the height as sides. You have only two variables, the side of the triangle and the height of the prism. Write the equation that computes the volume in terms of these and set it to $48$. Use that to eliminate one of the variables in the surface area equation, then differentiate, set to zero...
– Ross Millikan
Jul 28 at 4:02
add a comment |Â
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You need to define the variables in your surface area equation. Given that the bases are in the same orientation (definition of prism) and they are equilateral, the sides of the prism have the same area. They are rectangles with the side of the triangle and the height as sides. You have only two variables, the side of the triangle and the height of the prism. Write the equation that computes the volume in terms of these and set it to $48$. Use that to eliminate one of the variables in the surface area equation, then differentiate, set to zero...
– Ross Millikan
Jul 28 at 4:02