1.) A 2.5 x 2.5 x 2.5 meter hole was dug for the building's foundation. How many cubic meters of soil were dug?
2.) A cubical container is filled with 15,625 cm3 of sand. How long is each edge of the container?
3.) Kendy has 2 cardboard boxes. One has a dimension of 50x20x30 cm while the other has the dimension of 40x40x40 cm. Which box holds more space?
all of these are the same idea:
volume = length * width * height
1.) To find the number of cubic meters of soil that were dug, we need to calculate the volume of the hole. The volume of a rectangular prism (which is the shape of the hole in this case) can be found by multiplying its length, width, and height. In this case, the length, width, and height are all 2.5 meters. So, the volume of the hole would be calculated as follows:
Volume = length x width x height
= 2.5 m x 2.5 m x 2.5 m
= 15.625 cubic meters
Therefore, 15.625 cubic meters of soil were dug.
2.) The volume of a cube can be calculated by raising the length of one of its sides (edges) to the power of 3. In this case, we are given that the cube is filled with 15,625 cm3 of sand. So, to find the length of each edge of the container, we need to find the cube root of 15,625 cm3.
Edge length = cube root of volume
= cube root of 15,625 cm3
= 25 cm
Therefore, each edge of the container is 25 cm long.
3.) To determine which box holds more space, we need to compare their volumes. The volume of a rectangular prism can be calculated by multiplying its length, width, and height.
For the first box:
Volume = length x width x height
= 50 cm x 20 cm x 30 cm
= 30,000 cm3
For the second box:
Volume = length x width x height
= 40 cm x 40 cm x 40 cm
= 64,000 cm3
Comparing the volumes, we can see that the second box holds more space as its volume is 64,000 cm3 compared to the first box's volume of 30,000 cm3.