Volume of prisms

Question

1-elaine wants to make a net for a triangular prism using index cards. how many triangles will she need?

 

2-Tina cut open a cube-shaped microwave box to see the net. how many square faces does this box have?

 

3- Mr. Cooper purchased a night stand at the furniture store. It came in a rectangular-prism-shaped box. The volume of the box is 31,050 cubic inches. The box is 36 inches deep and 28 3/4 inches wide. What is the height of the box?

 

4- A box measures 6 units by 1/2 unit by 2 1/2 units. What is the greatest number of cubes with a side length of 1/2 unit that can be packed inside the box?

 

 

Answer 1

1) This question is just asking how many triangle-shaped faces there are in a triangular prism. Think about what a triangular prism looks like and count the number of triangle-shaped faces.

 

 

2) This question is just asking how many square-shaped faces there are in a cube. Think about what a cube looks like and count the number of square-shaped faces.

 

 

3) The formula for volume of a rectangular prism is V = (length)(width)(height). Plug in V = 31050, length = 36, and width = 28.75 and solve for height:

 

31050 = (36)(28.75)(width)

31050 = 1035(width)

30 = width

 

The width is 30 inches.

 

 

4) First, let's figure out how many cubic units the box can hold by computing its volume:

 

V = (length)(width)(height)

V = (6)(1/2)(2.5)

V = (3)(2.5)

V = 7.5 cubic units

 

Now, let's figure out how many cubic units a cube with side lengths of 1/2 unit fills:

 

V = (length)(width)(height)

V = (1/2)(1/2)(1/2)

V = (1/4)(1/2)

V = 1/8 cubic units

 

So, every cubic unit can hold 8 of the 1/2-side-length cubes. Multiply 7.5 by 8 to figure out how many cubes can fit in the box:

 

7.5(8) = 60 cubes