The formula for the volume of a cylinder is V equals pi r squared h. Which of the following is the same equation solved for the variable r
The Correct Answer and Explanation is:
To solve the equation for the variable r, start with the volume formula for a cylinder:V=πr2hV = \pi r^2 hV=πr2h
We need to isolate r. Here’s how to do it step-by-step:
- Divide both sides by πh\pi hπh: Vπh=r2\frac{V}{\pi h} = r^2πhV=r2 This gives us the equation: r2=Vπhr^2 = \frac{V}{\pi h}r2=πhV
- Take the square root of both sides: r=Vπhr = \sqrt{\frac{V}{\pi h}}r=πhV
So, the equation solved for r is:r=Vπhr = \sqrt{\frac{V}{\pi h}}r=πhV
Explanation:
The formula for the volume of a cylinder involves the radius, height, and the constant π\piπ. To solve for r, we start by isolating r2r^2r2, which means moving all other variables to the other side of the equation.
Dividing both sides by πh\pi hπh simplifies the right side of the equation, and we end up with the square of the radius, r2r^2r2, on the left side. Finally, to undo the squaring of rrr, we take the square root of both sides, which gives us the radius rrr in terms of the volume VVV and height hhh.
This manipulation is a common algebraic technique to isolate a variable in an equation. By following these steps, we can easily express rrr as a function of VVV and hhh, making it easier to calculate the radius when the volume and height of the cylinder are known.
