Here is a rectangle and a
square. They have the same width. The length of the rectangle is five
centimeters longer than its width. Four rectangles and two squares are
used to make this net. The perimeter of the 12-sided net
is 52 centimeters. Find the volume of the cuboid made
when the net is folded.
As the rectangle and the square
have the same width, we can let this equal 𝑥. As all four sides of a square are
equal, the length of the square will also be equal to 𝑥. As the length of the rectangle is
five centimeters longer than its width, an expression for the length would be 𝑥
We can now transfer these values
onto the diagram of the net. The perimeter of the net would be
calculated by adding the lengths of all the sides of the outside of the shape. As the perimeter of the net is 52
centimeters, we know that 12𝑥 plus 𝑥 plus five plus 𝑥 plus five is equal to
52. Grouping the like terms gives us
14𝑥 plus 10 is equal to 52 as 12𝑥 plus 𝑥 plus 𝑥 is equal to 14𝑥 and five plus
five is equal to 10. Subtracting 10 from both sides of
this equation gives us 14𝑥 is equal to 42. And finally, dividing both sides of
this equation by 14 gives us a value for 𝑥 equal to three.
This means that the square has
sides of three centimeters and the rectangle has a width of three centimeters and a
length of eight centimeters. The question asked us to find the
volume of the cuboid when the net is folded. The volume of any cuboid can be
calculated by multiplying the three dimensions: the length, the width, and the
height. In this case, we need to multiply
eight centimeters by three centimeters by three centimeters. Eight multiplied by three is 24 and
24 multiplied by three is 72.
Therefore, the volume of the cuboid
is 72 centimeters cubed.