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solong [7]
3 years ago
9

Compare the surface area-to-volume ratios of the moon and mars. express your answer using two significant figures.

Mathematics
2 answers:
antoniya [11.8K]3 years ago
5 0

we know that

For a spherical planet of radius r, the volume V and the surface area SA is equal to

V=\frac{4}{3} *\pi *r^{3} \\ \\ SA=4*\pi *r^{2}

The
ratio of these two quantities may be written as

SAV =\frac{(4*\pi*r^{2})}{(\frac{4}{3}*\pi*r^{3})}     \\  \\ SAV =\frac{3}{r}

we know

rMoon=1,738Km\\ rMars=3,397 Km

\frac{SAV Moon}{SAV Mars} =\frac{3}{rMoon} *\frac{rMars}{3} \\ \\ \frac{SAV Moon}{SAV Mars} =\frac{rMars}{rMoon} \\ \\ \frac{SAV Moon}{SAV Mars} =\frac{3,397}{1,738} \\ \\ \frac{SAV Moon}{SAV Mars} =1.9545

therefore

the answer is

1.9

FrozenT [24]3 years ago
5 0

The ratio of surface area to volume of the moon is \boxed{\bf 1.9\text{\bf\ times}} of the ratio of surface area to volume of the mars.

Further explanation:

The volume of the spherical shape can be calculated as,

\boxed{\text{Volume of sphere}=\dfrac{4}{3}\pi r^{3}}    

The surface area of the spherical shape can be calculated as,

\boxed{\text{Surface atrea of sphere}=4\pi r^{2}}  

Here, r is the radius of the sphere.

Calculation:

Step 1:

First we will calculate the ratio of surface area of the sphere to the volume of the sphere.  

The ratio of these quantities can be calculated as,

\begin{aligned}\dfrac{\text{Surface area}}{\text{Volume}}&=\dfrac{4\pi r^{2}}{\dfrac{4}{3}\pi r^{3}}\\&=\dfrac{3}{r}\end{aligned}    

Therefore, the ratio of the surface area to the volume of the sphere is \frac{3}{r}.

Step 2:

Second we will calculate the ratio of surface area of the moon to the volume of the moon.

The radius of the moon is 1738\text{ km}.

Substitute r=1738 in the ratio of the surface area to the volume of the sphere.

\begin{aligned}\dfrac{\text{Surface area of the moon}}{\text{Volume of the moon}}&=\dfrac{3}{r}\\&=\dfrac{3}{1738}\end{aligned}    

Step 3:

Third we will calculate the ratio of surface area of the mars to the volume of the mars.

The radius of the mars is 3397\text{ km}.

Substitute r=3397 in the ratio of the surface area to the volume of the sphere.

\begin{aligned}\dfrac{\text{Surface area of the mars}}{\text{Volume of the mars}}&=\dfrac{3}{r}\\&=\dfrac{3}{3397}\end{aligned}  

Step 4:

Now compare the ratios of the surface area to volume of moon with ratios of the surface area to volume of mars.

Divide the ratios of the moon by the ratio of the mars to compare.

\begin{aligned}\dfrac{\text{ratio for moon}}{\text{ratio for mars}}&=\dfrac{1738}{3}\times\dfrac{3}{3397}\\&=\dfrac{1738}{3397}\\&=1.9\end{aligned}  

Clearly we can see that the ratio surface area to volume of the moon is \boxed{\bf 1.9\text{\bf\ times}} of the ratio surface area to volume of the mars.

Learn more:  

1. A problem on equation of the circle brainly.com/question/1506955

2. A problem on distance, speed and timehttps://brainly.com/question/5424148

3. A problem on function brainly.com/question/9590016

Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Mensuration

Keywords: Mensuration, volume, surface area, sphere, ratio, moon, mars, comparision, spherical shape, curved surface area, radius of the sphere.

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