the volume of a rectangular prism is 2,058 cm3. The length of the prism is three times the width. The height is 14 centimeters. Find the other dimensions
2058 = 14 * w * 3 w
w^2 = 49
w = 7
L = 21
To find the other dimensions, we can start by finding the width of the rectangular prism.
Let's assume that the width of the prism is "w" cm.
According to the given information, the length of the prism is three times the width. So, the length would be 3w cm.
The height of the prism is given as 14 cm.
The formula to calculate the volume of a rectangular prism is:
Volume = Length × Width × Height
Substituting the given values, we have:
2058 cm³ = (3w cm) × (w cm) × (14 cm)
Now, we need to solve this equation to find the value of "w" (width).
2058 = 42w²
Dividing both sides by 42:
49 = w²
Taking the square root of both sides:
w = √49
Thus, w = 7 cm.
Since the length of the prism is three times the width, the length would be:
3w = 3 × 7 = 21 cm
Therefore, the width of the rectangular prism is 7 cm, the length is 21 cm, and the height is 14 cm.
To find the other dimensions of the rectangular prism, we need to use the given information and set up an equation.
Let's denote the width as "w," the length as "l," and the height as "h."
We know that the volume of the rectangular prism is 2,058 cm³. The formula for the volume of a rectangular prism is V = lwh.
So, we can write the equation as:
2,058 = lw * h
We are also given that the length of the prism is three times the width:
l = 3w
And the height is 14 centimeters:
h = 14
Now, substitute the value of l and h in terms of w into the equation to find the other dimensions:
2,058 = (3w) * w * 14
2,058 = 42w²
Rearrange the equation to isolate w:
42w² = 2,058
Divide both sides of the equation by 42:
w² = 2,058 / 42
w² ≈ 48.9
Take the square root of both sides:
w ≈ √48.9
w ≈ 6.99 (rounded to two decimal places)
Now, we have the value of the width, which is approximately 6.99 cm.
To find the length, multiply the width by 3:
l = 3 * 6.99
l ≈ 20.97 (rounded to two decimal places)
The length is approximately 20.97 cm.
Now that we have the width and length, we can calculate the volume using the formula V = lwh:
V = 20.97 * 6.99 * 14
V ≈ 2,058 cm³
Therefore, the dimensions of the rectangular prism are:
Width ≈ 6.99 cm
Length ≈ 20.97 cm
Height = 14 cm