If the edge of a cube is increased by 50%, then the volume is increased by x%. Find x.
PLEASE HELP.
THANK YOU.
Let Y = edge of a cube.
Y + 0.5Y = 1.5Y = new edge of the cube.
Then old volume is Y^3
New volume is (1.5Y)^3 = 2.375Y^3.
%increase = ([3.375Y^3 - Y^3]/Y^3) x 100 = x%. It looks like 237.5% to me but check it closely.
Try it with 1" cube changing to 1.5".
Or 2" cube changing to 3"
Or 3" cube changing to 4.5". I think all of those are 50% changes but check it out.
55
50%, 150%,
To find the value of x, we need to calculate the percentage increase in volume when the edge of the cube is increased by 50%.
Let Y be the length of the edge of the cube.
When the edge is increased by 50%, the new length becomes 1.5Y.
The volume V of a cube is calculated by V = Y^3.
The new volume V' after increasing the edge by 50% is calculated by V' = (1.5Y)^3.
To calculate the percentage increase, we need to find the difference between the new volume and the old volume, divided by the old volume, and then multiply by 100.
Percentage increase = ((V' - V) / V) x 100
Substituting the values, we have:
Percentage increase = (((1.5Y)^3 - Y^3) / Y^3) x 100
Simplifying this expression, we get:
Percentage increase = ((2.375Y^3 - Y^3) / Y^3) x 100
Therefore, the value of x, which represents the percentage increase, is given by:
x = ((2.375Y^3 - Y^3) / Y^3) x 100
In the given question, the value of x is not provided, so we cannot calculate it directly. However, by plugging in different values for Y and checking the corresponding percentage increase, we can determine the value of x.