Finding Radius from Volume
Grade 7 students in Big Ideas Math Advanced 2 (Chapter 8: Volume and Similar Solids) learn to find the radius of a sphere from its known volume by solving V = (4/3) pi r^3 for r. This inverse operation gives r = cube root of (3V / 4pi).
Key Concepts
To find the radius of a sphere when given its volume, solve the equation $V = \frac{4}{3}\pi r^3$ for $r$:.
$$r = \sqrt[3]{\frac{3V}{4\pi}}$$.
Common Questions
How do you find the radius of a sphere from its volume in 7th grade?
Use the formula r = cube root of (3V / (4 pi)). Multiply V by 3, divide by (4 pi), then take the cube root.
How do you find the radius if a sphere has volume 288 pi cubic units?
r = cube root of (3 x 288 pi / (4 pi)) = cube root of (864/4) = cube root of 216 = 6 units.
What is the sphere volume formula?
V = (4/3) pi r^3, where r is the radius. To find r from V, rearrange: r^3 = 3V / (4 pi), then r = cube root of (3V / (4 pi)).
What chapter in Big Ideas Math Advanced 2 covers finding radius from volume?
Chapter 8: Volume and Similar Solids in Big Ideas Math Advanced 2 (Grade 7) covers finding radius from volume.
When would you need to find radius from sphere volume?
When you know how much a spherical container holds (its volume) but need to determine its physical size (radius), such as designing a ball or spherical tank.