Answer:
length = 9.5 + 1 = 10.5 inches
height = 9.5 - 1 = 8.5 inches
width = 9.5 inches
Step-by-step explanation:
The questions want you to get the length, width and height of the cube.
let the width = y inches
length is 1 inch more than width . Therefore, length = y + 1
The width is 1 inch more than height. Therefore, height = y - 1
The formula volume for a cube = Length × breadth(width) × height
so, replacing your value in the formula;
volume = (y + 1) × y × (y-1)
recall the volume = 847.875
847.875 = y³ - y
Therefore y³- y - 847.875 = 0
solving the equation
(y²-1) × y = 847.875
y = 9.5
length = 9.5 + 1 = 10.5 inches
height = 9.5 - 1 = 8.5 inches
width = 9.5 inches
volume = 10.5 × 8.5 × 9.5 = 847.875 cubic inches
The length is one inch more than the width, which is one inch more than the height. The volume is 847.875 cubic inches. Thus, the actual length is 10.5 inches, the width is 9.5 in and the height is 8.5 in.
From the given information;
The length is one inch more than the width i.e.
Now, the width is one inch more than the height i.e.
Now, the length can written again as L = h + 1 + 1
The volume (v) = 847.875 in³
We all know that the volume (V) of a rectangle is:
SO;
Assuming h is the variable, then using h³ as a unit.
Then;
Finding the real roots of the above equation;
height = 8.5 inches
width = h + 1
width = 8.5 inches + 1
width = 9.5 inches
Length = w + 1
Length = 9.5 inches + 1
Length = 10.5 inches
Therefore, we can conclude that the height is 8.5 inches, the width is 9.5 inches and the length is 10.5 inches.
Learn more about the volume of a rectangle here:
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