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The diagram below shows the metal tin. the circumference of the top is eight pi centimetres calculate the amount of metal used to make this tin. The height of the tin is 8.5 cm

User Latchmi
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1 Answer

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Explanation:

since I can't see any diagram, I have to assume that the tin can is a regular cylinder. that means top and bottom circular areas have the same size and are parallel to each other.

the circumference of a circle is

2×pi×r

in our case that is 8×pi cm.

so, that means the radius is 8pi/2pi = 4 cm.

the amount of metal needed is simply the sum of all surface areas (top and bottom and the side wall / mantle).

the areas of the top and bottom are circles. the area of a circle is

pi×r²

so, in our case, one circle has

pi×4² = 16pi cm²

top and bottom together have then

2×16pi = 32pi

now for the mantle :

when you cut off the top and the bottom, cut the remaining mantle straight down in one line, and then place it flat on a table, you have a rectangle.

the length is the original circumference of the top/bottom circles, and the width is the original height of the cylinder.

the area of the mantle is therefore

8pi × 8.5 = 68pi cm²

that means in total the surface (and the amount of needed metal) of the tin can is

32pi + 68pi = 100pi cm² = 314.1592654... cm²

User Yic
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