Solving for the Radius of a Cylinder
To find the radius of a cylinder when volume and height are known, rearrange the volume formula V = pi r squared h to get r = square root of (V divided by pi h). For V = 72 pi cubic inches and h = 8 inches: r = square root of (72 pi divided by 8 pi) = square root of 9 = 3 inches. For V approximately 314 cubic meters and h = 4 meters: r = square root of (314 divided by 12.56) = square root of 25 = 5 meters. This algebraic reverse-formula skill from enVision Mathematics, Grade 8, Chapter 8 is essential for cylinder problems in 8th grade geometry.
Key Concepts
To find the radius of a cylinder when given the volume and height, rearrange the volume formula $V = \pi r^2 h$ to solve for $r$. $$r = \sqrt{\frac{V}{\pi h}}$$.
Common Questions
How do I solve for the radius of a cylinder?
Use r = square root of (V divided by pi h). Substitute the known volume V and height h, divide, then take the square root.
A cylinder has volume 50 pi cm cubed and height 2 cm. Find the radius.
r = square root of (50 pi divided by 2 pi) = square root of 25 = 5 cm.
A cylinder has volume approximately 628 m cubed and height 8 m. Find the radius (use pi = 3.14).
r = square root of (628 divided by (3.14 times 8)) = square root of (628 divided by 25.12) = square root of 25 = 5 m.
How is the formula r = square root of (V/pi h) derived?
Start with V = pi r squared h. Divide both sides by pi h: V/(pi h) = r squared. Take the square root: r = square root of (V/pi h).
What is a common mistake when solving for radius of a cylinder?
Forgetting to take the square root after dividing. After isolating r squared, you must take the square root to find r.
When do 8th graders learn to solve for cylinder radius?
Chapter 8 of enVision Mathematics, Grade 8 covers this in the Surface Area and Volume unit.