Question

i need the mass and density of a sphere made of solid glass with a 32 cm circumference.

Answer 1

Task i need the mass and density of a sphere made of solid glass with a 32 cm circumference. Solution:

Input Data $l = 32 \, \text{cm} = 0.32 \, \text{m}$ $\rho = 2200 \frac{\text{kg}}{\text{m}^3}$

Need to find: m

Solution:

The radius and circumference of a circle is related via the following formula.

From this formula, we find the radius of the circle and the radius of the sphere

$$l = 2 \pi r \rightarrow r = \frac {l}{2 \pi}$$

Volume of a sphere with a radius of the sphere is related by the following formula

$$V = \frac {4}{3} \pi r ^ {3}$$

Body weight is equal to the product of the density of the body on the amount of body:

$$m = \rho V = \frac {4}{3} \pi r ^ {3} \rho = \frac {4}{3} \pi \rho \left(\frac {l}{2 \pi}\right) ^ {3} = \frac {l ^ {3}}{6 \pi^ {2}} \rho = 1. 2 1 \mathrm {k g}$$

Answer: $1.21\mathrm{kg}$