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Published byLaila Frothingham Modified over 3 years ago

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GROUP’S MEMBERS NOR AINI MAT SAMAN NUR HANISAH ABDULLAH NOOR IZZATI TARMIZI INTAN IZAZI CHE ANI ‘WATERWORLD BEVERAGE CAN’

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Task As production manager of Waterworld Industry, you need to carry out an investigation on how to minimize the cost of material and hence maximize the profit.

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Role As production manager of Waterworld Industry, we need to determine the dimension of a can that make the minimize cost of materials.

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Goal To find the radius and the height of the cylindrical can when its total surface area is minimum.

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Solution Plan Step 1 We let the volume of the cylinder is 1.5L, so we can find the h We know that can is a cylinder, so the formula of cylinder is : Step 2

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We substitute value of h into formula of surface area A, We need to differentiate A to find the critical value Step 3 Step 4

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We need to equal the first differentiate with 0 to find the value of r Step 5

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We need to do second derivative to test either the value of r will give the minimum or maximum surface area If we get >0, its mean the value of r will get the minimum surface area. So we can find the value of h by substitute value of r Step 6 Step 7

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So we can find the minimum surface area Step 8

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Conclusion If we want to make a cylindrical can that hold 1.5 L of liquid, we need to use 6.2 cm for radius and 12.42 cm for height hence can minimize the cost of materials.

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12.42cm 6.2cm Area for circle Area for rectangle

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Thank you

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8.8: Optimum Volume and Surface Area

8.8: Optimum Volume and Surface Area

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