A cuboidal tin open at the top has dimensions 20 cm x 16 cm x 14 cm.

Question

A cuboidal tin open at the top has dimensions 20 cm x 16 cm x 14 cm. What is the total area of a sheet of metal required to make 10 such tins.

Answer 1

A cuboid has four sides (s) of equal area and two ends (e) of equal area. I'll assume that 20cm = length, 16cm = height and 14cm = width. The area of each side is 20cm x 16cm = 360cm² and the area of each end is 16cm x 14cm = 224cm². Since the top is open, then each cuboid has only three sides and two ends; and since there are 10 tins, then the total area is:

 

(3s + 2e)*10 = (3(360cm²) + 2(224cm²))*10

= (1080cm² + 448cm²)*10 = (1528cm²)*10

= 15,280 cm².

Answer 2

First of all, which dimension is the height?  That's important in order to figure out this problem.  Usually the dimensions are given as length x width x height.  Is that the case here? Let's assume it is.

 

So normally in a cuboid as you describe it, there would be 6 faces.  The two faces across from each other would be the same, so there would really be 2 equal sets of 3 different faces.  The area of each face would be the product of the specific dimensions that create that face.

 

What would the total area of this normal cuboid be?  Well just find the areas of all 3 different faces, and multiply the sum of that by 2.  So that gives 2 * (20*16 + 20*14 + 16*14) = 2 * (320 + 280 + 224) = 2 * (824) = 1648.

 

HOWEVER, in this tin the top is open!  So you have to remove the area that would have been taken by the top.  Since we are assuming that the height is 14, the area of the top face would be the product of the other two dimensions, 20 * 16 = 320.  So subtract 320 from 1648 to get the total area of metal that is actually needed in each tin.  So the result is 1328.

 

Now multiply that by 10 to get the total area of sheet metal required for 10 tins:  13280 cm³

Answer 3

The tin has six faces.

Two are 14x20, or 2(280) cm², or 560 cm².

Two are 16x20, or 2(320) cm², or 640 cm².

Two are 14x16, or 2(224) cm², or 448 cm².

 

The surface area of one tin is 1648 cm².

For ten tins the area is 16480 cm².