Volume of a cylinder is 15 cubic inches. If all the dimensions are multiplied by 2.7 what is the new volume?
To find the new volume of the cylinder when all dimensions are multiplied by 2.7, we need to understand the formula for the volume of a cylinder.
The formula for the volume of a cylinder is V = πr^2h, where V represents the volume, π is pi (approximately 3.14159), r is the radius of the base, and h is the height of the cylinder.
Given that the volume of the original cylinder is 15 cubic inches, we can set up the equation: 15 = πr^2h.
If all dimensions are multiplied by 2.7, the new radius (r') will be 2.7r, and the new height (h') will be 2.7h. So, we can rewrite the equation with the new dimensions: V' = π(2.7r)^2(2.7h).
To find the new volume, we need the value of π and the original radius (r) and height (h). Let's assume π is approximately 3.14159, and we'll leave the original dimensions as unknowns for now.
V' = 3.14159(2.7r)^2(2.7h)
Next, we can expand and simplify the terms inside the parentheses:
V' = 3.14159(7.29r^2)(7.29h)
Now, we can simplify further and multiply the terms:
V' = 153.938(r^2)(h)
Finally, we have the new volume expressed in terms of the original dimensions. To calculate the new volume, substitute the values of the original dimensions into the equation.