If the volume of a cylinder is 150 cubic centimeters and the height is 10 cm, what is the radius of the base?

To find the radius of the base of the cylinder, you can use the formula for the volume of a cylinder: \( V = \pi r^2 h \). Rearranging for the radius, you get \( r^2 = \frac{V}{\pi h} \). Plugging in the values, \( V = 150 \) cm³ and \( h = 10 \) cm, gives \( r^2 = \frac{150}{\pi \times 10} \), which simplifies to \( r^2 = \frac{15}{\pi} \). This results in \( r ≈ 2.18 \) cm after taking the square root. Did you know that cylinders have been used since ancient times? The earliest known use dates back to Mesopotamian architecture, where these shapes helped create grand structures with both stability and beauty. Today, you can see the concepts of cylindrical design in everything from drink cans to high-rise buildings! Understanding cylinders also has practical applications in engineering and manufacturing! For instance, knowing the volume helps in determining the amount of liquid a tank can hold or calculating the material needed for producing cylindrical parts. It's essential to be accurate with measurements to avoid any costly errors in production and design!