Compare the surface area-to-volume ratios of the earth and venus.

Physics

2 answers:

jenyasd209 [6]4 years ago

4 0

<span>Venus has a larger surface area to volume ratio than Earth. The actual ratios are 0.000495704 for Venus and 0.000470884 for Earth. This is an example of the cube/square law. As an object increases in size, it's volume increases as a function of the cube of the radius while the surface area increases as a function of the square of the radius. Take a look at the formula for the volume of a sphere and then the formula for the surface area of a sphere. volume = (4/3)pi * r^3 area = 4*pi*r^2 So let's apply these formulas to Earth and Venus Radius Earth = 6371 km Radius Venus = 6,052 km Right off the bat without doing any calculations, Venus will have a higher surface area to volume ratio than Earth. Let's confirm that. Earth volume = (4/3)pi * r^3 = (4/3)pi * (6371 km)^3 = 1.08321x10^12 km^3 Venus volume =(4/3)pi * r^3 = (4/3)pi * (6052 km)^3 = 9.28507x10^11 km^3 Earth surface = 4*pi*r^2 = 4*pi*(6371 km)^2 = 510064471.9 km^2 Venus surface = 4*pi*r^2 = 4*pi*(6052 km)^2 = 460264736.8 km^2 Earth surface area/volume ratio = 510064471.9 / 1.08321x10^12 = 0.000470884 Venus surface area/volume ratio = 460264736.8 / 9.28507x10^11 = 0.000495704</span>

padilas [110]4 years ago

4 0

The ratio of the surface area to the volume of the Earth is $\fbox{0.94989}$ times the ratio of the surface area to the volume of the Venus.

Further Explanation:

As the size of the planet is very large enough, the gravity pull all the matters or materials the planets composed of like rock, containing common minerals like group of rock-forming tectosilicate minerals and metals like magnesium and aluminumetc. toward the center of the mass of the earth or toward the core of the planet.

Given:

The radius of the Earth is 6371 km.

The radius of the Venus is 6051.8 km.

Concept:

The shape of the Earth and the Venus is considered as sphere. So, the formula for volume of the Earth and the Venus is same as sphere.

The formula for surface area of the sphere is given by:

$\boxed{A=4\pi{R^2}}$

Here, $R$ is the radius of the spherical body.

The formula forvolume of the sphere is given by:

$\boxed{V=\dfrac{4}{3}\pi{R^3}}$

The ratio of the surface area to the volume of the sphere is:

$\begin{aligned}\dfrac{A}{V}&=\dfrac{{4\pi{R^2}}}{{\dfrac{4}{3}\pi{R^3}}}\\&=\frac{3}{R}\\\end{aligned}$

Substitute $6371\text{ km}$ for $R$ in the above expression.

$\dfrac{A}{V}=\dfrac{3}{{6371{\text{ km}}}}$

Therefore, the ratio of the surface area to the volume of the Earth is $\dfrac{3}{{6371{\text{ km}}}}$ .

Substitute $6051.8\text{ km}$ for $R$ in the above expression.

$\dfrac{A}{V}=\dfrac{3}{{6051.8{\text{ km}}}}$

Therefore, the ratio of the surface area to the volume of the Venus is $\dfrac{3}{{6051.8{\text{ km}}}}$ .

To compare the ratio of the surface area to the volume of the Earth and the ratio of the surface area to the volume of the Venus, we divide the ratio of the surface area to the volume of the Earth to ratio of the surface area to the volume of the Venus.

Therefore, it can be written as.

$\begin{aligned}\dfrac{\left(\dfrac{A}{V}\right)_E}{\left(\dfrac{A}{V}\right)_V}&=\dfrac{{\dfrac{3}{{6371{\text{ km}}}}}}{{\dfrac{3}{{6051.8{\text{ km}}}}}}\\&= 0.94989\end{aligned}$