The radius of the cylindrical cup can be determined by using the formula for the volume of a cylinder and solving for the radius. Given the volume and height, the radius is calculated, and then it is rounded to the nearest hundredth to match the provided options.
To find the radius of the cylindrical cup, we can use the formula for the volume of a cylinder, which is V = πr²h, where V represents the volume, r is the radius, and h is the height of the cylinder. In this case, we are given the volume (V = 480 cm³) and the height (h = 8 cm) of the cylinder. By substituting these values into the formula and solving for the radius r, we can find the desired radius of the cup.
Plugging in the values, we get:
480 = πr²(8). To isolate r², we divide both sides by 8π.
This gives us r² = ⅔π, and taking the square root of both sides gives us the radius. Calculating the exact value and rounding to the nearest hundredth will give us the answer to which option it corresponds.