The height of a cylinder is 4 millimeters. The circumference of its base is \( 10 \pi \mathrm{~mm} \) What is the radius: What is the volume to the nearest tenth:

To find the radius of the cylinder, we use the circumference formula: \( C = 2\pi r \). Given that the circumference is \( 10\pi \mathrm{~mm} \), we can set up the equation \( 2\pi r = 10\pi \). Dividing both sides by \( 2\pi \), we find that \( r = 5 \mathrm{~mm} \). Now, to calculate the volume of the cylinder, we can use the formula \( V = \pi r^2 h \). Plugging in our values \( r = 5 \mathrm{~mm} \) and \( h = 4 \mathrm{~mm} \), we get \( V = \pi (5^2)(4) = \pi (25)(4) = 100\pi \mathrm{~mm}^3 \). To the nearest tenth, the volume is approximately \( 314.2 \mathrm{~mm}^3 \).