Question

One sphere has a radius of 5.10 cm; another has a radius of 5.00cm. What is the difference in volume (in cubic centimeters) between the two spheres? The volume of the sphere is (4/3)*pi*r^3, where pi=3.1416. How do you know?

Answer 1

By definition, the volume of a sphere is given by:

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

Where,

r: sphere radio

Therefore, the difference between the volume of the two sphere is given by:

$V1 - V2 = (\frac{4}{3}) * \pi * r1 ^ 3 - (\frac{4}{3}) * \pi * r2 ^ 3$

Rewriting we have:

$V1 - V2 = (\frac{4}{3}) * \pi * (r1 ^ 3 - r2 ^ 3)$

Substituting values we have:

$V1 - V2 = (\frac{4}{3}) * 3.1416 * (5.10 ^ 3 - 5 ^ 3)\\V1 - V2 = 32.05 cm ^ 3$

Answer:

The difference in volume (in cubic centimeters) between the two spheres is:

$V1 - V2 = 32.05 cm ^ 3$

Answer 2

$\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}\qquad \begin{cases} r=radius\\ -----\\ r_1=5.10\\ r_2=5 \end{cases}\implies \cfrac{V_1}{V_2}\implies \cfrac{\frac{4\pi \cdot 5.10^3}{3}}{\frac{4\pi \cdot 5^3}{3}} \\\\\\ \cfrac{\underline{4\pi }\cdot 5.10^3}{\underline{3}}\cdot \cfrac{\underline{3}}{\underline{4\pi }\cdot 5^3}\implies \cfrac{5.10^3}{5^3}\implies \cfrac{132.651}{125}$