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Finding the Dimension of a Soft Drink Can

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by

Arthur Nonay

on 20 February 2013

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Transcript of Finding the Dimension of a Soft Drink Can

Created by Arthur Nonay Dimensions of a Soft Drink Can Question 1: Question 3 Height of a Can with a Diameter of 66mm
and a Volume of 355mL. Finding the Height of a Can with a Diameter of 56 mm and a Volume of 355 mL. Question 2 Question 4: Surface area of cans in questions 1 & 2 Least materials in a 355mL can Volume = Area of Base x Height Area of Base = Pi x (Radius Squared) Radius = Diameter/2 66/2 = 33 33^2 = 1,089 1,089 x Pi = 3,420.529mm^2 1 mL = 1 cm^3 355mL = 355cm^3 3,420.529/100 = 34.20529 cm^2 355/34.2 = 10.38 cm The Answer 355 mL = 355 cm^3 Area of Base: pi x (radius squared) Radius: 56/2 = 28 mm 28^2 = 784 784 x pi = 2463 Convert to Centimetres: 2463/100 = 24.63 cm 355/ 24.63 = 14.4 cm The Answer: 14.4 cm 1: 3.3cm = radius Formula: (2 x pi x radius) x height) + (2 x area of base) 10.38cm = height 2 x pi x 3.3 = 20.7 cm 20.7 x 10.38 = 214.9 34.2cm ^ 2 = area 2 x 34.2 = 68.4 cm ^ 2 The surface area of the can in question 1 is 283.3 cm ^2 214.9 + 68.4 = 283.3 2: 2.8 cm = radius 14.4 cm = height 24.63cm ^ 2 = area 2 x pi x 2.8 = 17.6cm 17.6 x 14.4 = 253.4 2 x 24.63 = 49.26cm ^ 2 253.4 + 49.26 =302.66 The surface area of the can in question 2 is 302.66 cm ^ 2 To find the least amount of materials required, you would want the can as cuboid as possible, so I will find the cube root of 355mL. 3^ 355 = 7.1cm Use 7.1 as the height and diameter. 7.1/2 = 3.55 = radius pi x (3.55^2) = 39.6 Area of Base is equal to this equation. 39.6 x 7.1 = 281.2 This is incorrect. Add more to the height by dividing 355 by the area of the base, or 39.6. 355/39.6 = approximately 9 (8.96) Check: 39.6 x 9 = 356.4, so the answer is correct! The End
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