the dimensions of trianguloar prism A andtriangular prism B are proportional. The volume of the Triangular Prism is 6,400 cubic feet. If the volume of Triangular prism B is 75% of the volume of Triangular Prism B. What is the volume of Trianguloar Prism B?
.75 * 6400 = ?
4800.
Right!
To find the volume of Triangular Prism B, we need to determine the proportion of the dimensions between Prism A and Prism B and apply it to the given volume of Prism A.
Let's assume the dimensions of Triangular Prism A are represented by length A, width A, and height A. Similarly, the dimensions of Triangular Prism B are represented by length B, width B, and height B.
We know that the dimensions of Prism A and Prism B are proportional. This means that we can write the following ratios:
length A / length B = width A / width B = height A / height B
Let's assume the common ratio of the proportions is represented by k.
Next, we are given that the volume of Triangular Prism A is 6,400 cubic feet.
Volume A = length A * width A * height A = 6,400
Now, we know that the volume of Prism B is 75% of the volume of Prism A.
Volume B = 0.75 * Volume A
= 0.75 * 6,400
To find the volume of Prism B, we need to determine the value of k (the common ratio of the proportional dimensions). To do this, we can make use of the fact that the volume of a prism is directly proportional to the product of its dimensions.
Since Volume A = length A * width A * height A, and Volume B = 0.75 * Volume A, we can write:
length B * width B * height B = k * (length A * width A * height A)
= k * 6,400
Now, we can rearrange the equation to solve for the volume of Prism B:
Volume B = length B * width B * height B
= k * (length A * width A * height A)
= k * 6,400
Therefore, the volume of Triangular Prism B is k * 6,400 cubic feet, where k represents the common ratio of the proportional dimensions.