Volume of prisms.

[Ams627]

Based on a perpendicular triangular prism ABCDEF with a height of 10 cm is an isosceles triangle ABC whose area is 12 cm2, the perimeter is 16 cm and the length of the base AB is 6 cm.

What is the surface area of the prism? What is the volume of the prism?

[Ams627]

The surface area of a regular quadrilateral prism is 144 cm²

The surface area of a regular quadrilateral prism is 144 cm2 . The shell are of this prism is twice the area of one of its square bases. (The shell of this prism consists of four congruent side walls.)

7 Calculate 7.1 in cm length of the side of the square base, 7.2 in cm² the area of one side wall of the prism, 7.3 in cm³ volume of the prism.

Solution: If base is 𝑥 cm2 then the shell is 2𝑥 cm2 and the total surface are is 4𝑥 cm2.

So the shell is 72 cm2 and the base is 36 cm2. One side wall is 72/4 cm2 which equals 18 cm2.

Using one side wall as the base, we get the volume as 18 x one side of the square. or 18x6 cm3 which is 108 cm3.

What is the slightly difficult here? It may be difficult to see that the side wall can be used as a base. We don't know the "height of the pyramid as it is shown in the diagram, so we have to use one edge of the square as the height.

[Ams627]

Solution: If base is 𝑥 cm² then the shell is 2𝑥 cm² and the total surface are is 4𝑥 cm².

So the shell is 72 cm² and the base is 36 cm². One side wall is 72/4 cm² which equals 18 cm².

Using one side wall as the base, we get the volume as 18 x one side of the square. or 18x6 cm³ which is 108 cm³.

What is the slightly difficult here? It may be difficult to see that the side wall can be used as a base. We don't know the "height of the pyramid as it is shown in the diagram, so we have to use one edge of the square as the height.

[Ams627]

The upper part of the glass block consists of 6 colored glass cubes placed in one layer. Each cube has an edge of length 2 cm. The same layer of cubes also forms the lower part of the cuboid. Both layers of colored cubes together occupy 20% of the volume the entire block. The rest of the block is made of white glass.

7 Calculate 7.1 in cm3 volume of one layer of colored cubes, 7.2 in cm the length of the longest edge of the entire cuboid, 7.3 in cm2 the surface of the entire block. In the recording sheet, indicate the solution procedure in all parts of the problem.