The width of a rectangular prism is 30 cm. This is 12 more than one-fourth of the length. Find the volume of the prism, given the height, is 20 cm.
P.S. I need this question by 01-26-18
To find the volume of the rectangular prism, we need to know the length, width, and height. Let's start by finding the length using the information given.
According to the problem, the width of the prism is 30 cm, which is 12 more than one-fourth of the length. Let's represent the length with the variable "L". We can write the equation as:
30 = (1/4)L + 12
To isolate L, we can subtract 12 from both sides:
30 - 12 = (1/4)L
18 = (1/4)L
To solve for L, we can multiply both sides by 4:
4 * 18 = L
72 = L
So, the length of the prism is 72 cm.
Now that we have the length (L = 72 cm), width (W = 30 cm), and height (H = 20 cm), we can calculate the volume of the rectangular prism using the formula:
Volume = Length × Width × Height
Substituting the known values, we get:
Volume = 72 cm × 30 cm × 20 cm
Volume = 43200 cm³
Therefore, the volume of the rectangular prism is 43200 cubic centimeters.
30 - 12 = L/4
18 = L/4
L = 4*18
V = 30 * 4*18 * 20