Multiply the edge lengths of a right rectangular prism with the length of 1/2 m width 1/4 m and lenght 5/4 cm to show that the product is the same as the volume found by packing the prism with 10 unit cubes with an edge of 1/4 m what is the volume of the prism
Sure, let's solve this step by step.
The given dimensions of the right rectangular prism are:
Length = 1/2 m
Width = 1/4 m
Height = 5/4 cm
To find the product of the edge lengths, we multiply them:
(1/2 m) x (1/4 m) x (5/4 cm)
We can simplify the units by converting cm to m:
(1/2 m) x (1/4 m) x (0.0125 m)
= 0.00078125 m^3
This is the volume of the prism using the edge lengths formula.
Now, let's find the volume of the same prism by packing it with 10 cubes of edge length 1/4 m.
Each cube has a volume of:
(1/4 m) x (1/4 m) x (1/4 m) = 0.015625 m^3
The total volume of 10 such cubes is:
10 x 0.015625 m^3 = 0.15625 m^3
This is the volume of the prism using the packing method.
We can see that both methods give the same volume of the prism. Therefore, the answer is:
Volume of the prism = 0.15625 m^3.
What is 0.15625 m^3 as a fraction
To write 0.15625 m^3 as a fraction, we need to convert the decimal to a fraction. Here's how:
0.15625 can be written as the fraction 15625/100000 in its simplest form.
To simplify this fraction, we can divide both the numerator and denominator by 15625, which gives:
15625/100000 รท 15625/15625 = 1/6.4
Therefore, 0.15625 m^3 can be expressed as the fraction 1/6.4.
To find the volume of a right rectangular prism, we simply multiply the length, width, and height together.
First, let's find the edge lengths of the prism. According to the given information, the width is 1/4 m, the length is 5/4 cm, and the height is 1/2 m.
Since we need to multiply dimensions with consistent units, we need to convert the length to meters:
1 cm = 0.01 m
Therefore, the length in meters will be:
(5/4) cm * (0.01 m / 1 cm) = (5/4) * 0.01 m = 0.0125 m
Now we can calculate the volume of the prism by multiplying the edge lengths:
Volume = (0.0125 m) * (1/4 m) * (1/2 m) = 0.0125 * 0.25 * 0.5 = 0.0015625 m^3
Now, let's find the volume by packing the prism with 10 unit cubes with an edge length of 1/4 m. The volume of a cube is equal to the length raised to the power of 3.
Volume of a cube = (1/4 m)^3 = (1/4 m) * (1/4 m) * (1/4 m) = 1/64 m^3
To find the volume of 10 cubes, we multiply the volume of a single cube by 10:
Total volume = (1/64 m^3) * 10 = 10/64 m^3 = 0.15625 m^3
As we can see, the product of the edge lengths of the prism is equal to the volume calculated by packing the prism with 10 unit cubes. Therefore, the volume of the prism is 0.15625 m^3.