Height as a Function of Volume in a Cylinder
Grade 8 math students learn to find the height of a cylinder given its volume and radius by rearranging the formula V = pi*r^2*h to get h = V / (pi*r^2). This skill involves substituting known values and solving for the missing dimension. Covered in Big Ideas Math, Course 3, Chapter 8: Volume and Similar Solids.
Key Concepts
To find the height ($h$) of a cylinder given its volume ($V$) and radius ($r$), you can rearrange the volume formula $V = \pi r^2 h$. By dividing both sides by the area of the base, $\pi r^2$, we get the formula for height: $$h = \frac{V}{\pi r^2}$$.
Common Questions
How do you find the height of a cylinder given its volume?
Rearrange the cylinder volume formula V = pi*r^2*h by dividing both sides by pi*r^2 to get h = V / (pi*r^2). Substitute the known volume and radius values and calculate.
What is the formula for the height of a cylinder?
The height of a cylinder can be found using h = V / (pi*r^2), which is derived by rearranging the standard volume formula V = pi*r^2*h and solving for h.
How do you solve for a missing dimension of a cylinder?
If you know the volume V and radius r of a cylinder, use h = V / (pi*r^2). If you know the diameter instead of radius, first divide diameter by 2 to get r, then substitute into the formula.
Which textbook covers cylinder height from volume for Grade 8?
This topic is in Big Ideas Math, Course 3, Chapter 8: Volume and Similar Solids.
What grade level covers cylinder volume and height?
Finding the height of a cylinder from its volume is typically covered in Grade 8 math.