Final answer:
The volume and surface area of a marble with a 10 mm radius are approximately 4186.67 mm³ and 1256.00 mm², respectively, using 3.14 for π and rounding to the nearest hundredth.
Step-by-step explanation:
Calculating Volume and Surface Area of a Marble
To find the volume and surface area of a marble with a radius of 10 millimeters using 3.14 for π (pi), we first use the formula for the volume of a sphere, which is 4/3 πr³. By plugging in the radius (r = 10 mm), we get:
Volume (V) = 4/3 × 3.14 × (10 mm)³
Calculating this gives us:
V = 4/3 × 3.14 × 1000 mm³
V = 4186.67 mm³
Next, to find the surface area of the marble, we use the formula for the surface area of a sphere, which is 4 πr². Plugging in the radius again gives us:
Surface area (A) = 4 × 3.14 × (10 mm)²
A = 4 × 3.14 × 100 mm²
A = 1256 mm²
After rounding both values to the nearest hundredth, we have the results:
Volume: 4186.67 mm³ → 4186.67 mm³
Surface area: 1256 mm² → 1256.00 mm²
The actual calculation might yield more precise numbers due to more digits in π, but as we're using 3.14 and rounding to the nearest hundredth, these are the approximate results.