The shorter edges of a 36 cm x 20 cm metalsheet are joined to form the vertical surfaces of a square base prism. What is the volume of the prism? what is the area of metal sheet required to make the top and the bottom of the prism.
height = 20
side length = 36/4 = 9
volume = 9*9*20 cm^3
top = 81 cm^2
bottom = 81 cm^2
81 * 2 = 162 cm^2
Hmmm. Hard to see.
The length is 36 and the width is 20.
If the height of the box is x, then the base would be 18-x. With the other edge width=20, I don't see how the base can be square.
I think it is just folded three times so the short edges can be welded together. No top and bottom yet
To find the volume of the prism, you need to know the length, width, and height of the prism.
In this case, the shorter edges of the metal sheet (which are 20 cm) are joined to form the vertical surfaces of the base. This means that the length and width of the base of the prism are both 20 cm.
The metal sheet is then folded to form the sides and top of the prism. The length of the prism will be 36 cm.
Since the base of the prism is a square with sides of 20 cm, the height of the prism is also 20 cm (since it is a right prism).
To find the volume of the prism, you multiply the length, width, and height:
Volume = Length x Width x Height
Volume = 36 cm x 20 cm x 20 cm
Volume = 14,400 cm^3
So, the volume of the prism is 14,400 cubic centimeters.
To find the area of the metal sheet required to make the top and bottom of the prism, you need to find the area of two squares, one for the top and one for the bottom, with sides of 20 cm.
The area of a square can be found by squaring the length of one side:
Area of square = Side x Side
Area of square = 20 cm x 20 cm
Area of square = 400 cm^2
Since there are two squares (one for the top and one for the bottom), the total area of the metal sheet required is:
Total area = 2 x Area of square
Total area = 2 x 400 cm^2
Total area = 800 cm^2
So, the area of metal sheet required to make the top and bottom of the prism is 800 square centimeters.