Question

a student is given a metal sphere about the size of a softball and asked to identify what type of metal it is made of. it has a radius of 5.00 cm and a mass of 5.915 kg. first identify what the density is. 5.915 4/3 1000 11.3 3.14 5.00 524 1 5915

Explanation:

Step1: Calculate Volume of Sphere

The formula for the volume of a sphere is \( V = \frac{4}{3}\pi r^3 \). Given \( r = 5.00 \, \text{cm} \), substitute:
\( V = \frac{4}{3} \times \pi \times (5.00)^3 \approx \frac{4}{3} \times 3.1416 \times 125 \approx 523.598 \, \text{cm}^3 \approx 524 \, \text{cm}^3 \) (but we'll use exact steps for density).

Step2: Convert Mass to Grams

Mass \( m = 5.915 \, \text{kg} = 5915 \, \text{g} \) (since \( 1 \, \text{kg} = 1000 \, \text{g} \)).

Step3: Calculate Density

Density \(
ho = \frac{m}{V} \). First, compute \( V \) precisely:
\( V = \frac{4}{3}\pi (5.00)^3 = \frac{4}{3}\pi \times 125 \approx 523.598 \, \text{cm}^3 \).
Then, \(
ho = \frac{5915 \, \text{g}}{523.598 \, \text{cm}^3} \approx 11.3 \, \text{g/cm}^3 \).

Answer:

11.3