Use the image to answer the question
Decompose the box net into simple polygons to find how much cardboard in square inches is needed to make the cube. Assume that all angles that look like right angles are right angles. All polygons that look congruent are congruent. What is the area of the shape in square inches?
To find the total area of the net, we need to calculate the areas of each of the simple polygons and then add them together.
1. The bottom square has a side length of 6 inches, so its area is 6 * 6 = 36 square inches.
2. There are two rectangles on the sides, each with dimensions of 6 by 1.5 inches. So each rectangle has an area of 6 * 1.5 = 9 square inches. Since there are two of them, the total area for the rectangles is 2 * 9 = 18 square inches.
3. There are four small squares on the top and sides, each with a side length of 1.5 inches. So the area of each square is 1.5 * 1.5 = 2.25 square inches. Since there are four squares, the total area for the small squares is 4 * 2.25 = 9 square inches.
Adding all these areas together:
36 (square inches for the bottom square) + 18 (square inches for the rectangles) + 9 (square inches for the small squares) = 63 square inches
Therefore, the total amount of cardboard needed to make the cube is 63 square inches.
Question 2
Find the volume of the right rectangular prism.
To find the volume of the right rectangular prism, we need to multiply the length, width, and height of the prism together.
Looking at the net of the prism, we can see that the dimensions are as follows:
Length = 6 inches
Width = 6 inches
Height = 1.5 inches
To find the volume, multiply these dimensions together:
Volume = Length * Width * Height
Volume = 6 * 6 * 1.5
Volume = 54 cubic inches
Therefore, the volume of the right rectangular prism is 54 cubic inches.
Question 3
What is the volume of the right rectangular prism packed with 10 cubes? Each cube has an edge length of 1/3 meter
First, let's convert the edge length of each cube from meters to inches:
1 meter is equal to 39.3701 inches
Therefore, the edge length of each cube is 1/3 meter * 39.3701 inches/meter ≈ 13.1237 inches
Now, we need to find the volume of one small cube:
Volume of one cube = (Side length)^3
Volume of one cube = (13.1237)^3 ≈ 225.4123 cubic inches
Next, we need to find the total volume of 10 cubes in the prism:
Total volume = Volume of one cube * Number of cubes
Total volume = 225.4123 cubic inches * 10
Total volume = 2254.123 cubic inches
Therefore, the volume of the right rectangular prism packed with 10 cubes is approximately 2254.123 cubic inches.
Question 4
Multiply the edge lengths of a right rectangular prism with length 1/2 m, width 1/4 m, and height 5/4 m to show that the product is the same as the volume found by packing the prism with 10 unit cubes with an edge length of 1/4 m. What is the volume of the
First, let's calculate the volume of the right rectangular prism with edge lengths of 1/2 m, 1/4 m, and 5/4 m:
Volume = Length * Width * Height
Volume = (1/2) * (1/4) * (5/4)
Volume = 5/64 cubic meters
Next, let's calculate the volume of the unit cubes with an edge length of 1/4 m:
Volume of one unit cube = (1/4)^3
Volume of one unit cube = 1/64 cubic meters
Now, we need to find the total volume of 10 unit cubes in the prism:
Total volume = Volume of one unit cube * Number of cubes
Total volume = (1/64) * 10
Total volume = 10/64 cubic meters
Total volume = 5/32 cubic meters
Therefore, the product of the edge lengths of the right rectangular prism is 5/64 cubic meters, which is the same as the volume found by packing the prism with 10 unit cubes with an edge length of 1/4 m, which is also 5/32 cubic meters.