Finding the height of a cone given volume and radius
Finding the height of a cone given its volume and radius is a Grade 7 algebra and geometry skill in Big Ideas Math Advanced 2, Chapter 8: Volume and Similar Solids. By rearranging the cone volume formula V equals one-third pi r squared h, the height can be isolated as h equals 3V divided by pi r squared. For example, a cone with volume 84 pi cubic inches and radius 6 inches has a height of 7 inches.
Key Concepts
To find the height of a cone when given its volume and radius, solve the cone volume formula $V = \frac{1}{3}\pi r^2 h$ for $h$: 1. Start with the cone volume formula: $V = \frac{1}{3}\pi r^2 h$ 2. Multiply both sides by 3: $3V = \pi r^2 h$ 3. Divide both sides by $\pi r^2$: $h = \frac{3V}{\pi r^2}$.
Common Questions
How do you find the height of a cone when given its volume and radius?
Rearrange the cone volume formula by multiplying both sides by 3 and dividing by pi times r squared: h equals 3V divided by (pi times r squared). Substitute the known values to solve.
What is the formula for cone height given volume and radius?
h equals 3V divided by pi r squared. This is derived by solving the cone volume formula V equals one-third pi r squared h for h.
How do you rearrange the cone volume formula?
Start with V equals one-third pi r squared h. Multiply both sides by 3 to get 3V equals pi r squared h, then divide both sides by pi r squared to isolate h.
What textbook covers finding cone height from volume in Grade 7?
Big Ideas Math Advanced 2, Chapter 8: Volume and Similar Solids covers solving cone volume formulas for missing dimensions.