Question

A company manufactures aluminum mailboxes in the shape of a box with a half-cylinder top. The company will make mailboxes this week. If each mailbox has dimensions as shown in the figure below, how many square meters of aluminum will be needed to make these mailboxes? In your calculations, use the value for , and round up your answer to the next square meter

Answer 1

is there an SS provided for this question?

Answer 2

it says 1470 mailboxes and to use 3.14 for pie

Answer 3

well, we know that pi is equal to 3.1459

Answer 4

the mailboxes are hollow. so we only need aluminium for the surfaces. therefore, we only need the outside surface area of the mailbox.

for the two sides at the front and back, the area is WH each (so 2WH total)
for the two long sides on the left and right, the area is LH each (so 2LH total)
for the bottom of the mailbox, the area is WL (only WL. the ceiling of the mailbox is the curved part, which we'll calculate next)

for the curved part, it's a half cylinder. therefore, it's surface area is (1/2) * 2 * pi*r*h = pi * (1/2 W)*L

finally, we add two semicircles to get one full circle. the radius of the circle is (1/2)W. so area of the circle is pi*(r)^2 = pi*(1/2 W)^2

add up the surfaces to get the amount of aluminum to make 1 mailbox. multiply by 1470 to get the area of all the mailboxes.