The Earth Is To A Soccer Ball, As The Moon Is To What?

Let x be the size of the ball.

$\frac{11}{6368} = \frac{x}{1738}$

Use MPE to transfer 1738 to the other side and multiply it to 11. Divide it by 6368. You get a product of 3.00..... That is why it is a tennis ball.

This problem is a problem of ratio and proportions. Let the ratio of radii of moon to radii of Earth be $R_{ME}$

Then, we have -----> $R_{ME}=\frac{\text{Radii of Moon}}{\text{Radii of Earth}}=\frac{1738\text{ km }}{6368 \text{ km }}\approx \boxed{0.27}$

Now, for the best representation, this ratio must be maintained closely. So-----

Let the new radii of Earth (as football) be $R_e$ and new radii of moon be $R_m$ . So-----

$\frac{R_m}{R_e}=R_{ME} \implies \frac{R_m}{11\text{ cm}}=0.27 \implies R_m=\boxed{2.97\text{ cm}}$

The best representation model for the moon with respect to the Earth model (football) should be the one having a radii close to 2.97 cm and we can see that Tennis ball $(r\approx 3 \text{ cm })$ is the best representation for the Moon.

So, the answer should be Tennis ball $(r\approx 3 \text{ cm })$

1738:6368=x:11.. it can be solve through that formula..the ratio and proportion

Let radius of ball representing moon be x Ratio of radii of moon and earth = ratio of radii of both balls radius of moon/radius of earth = x/11 x = 11 x radius of moon/radius of earth x = 11 x 1738/6368=11 x 869/3184=9559/3184=3.002................................... Therefore radius of ball representing moon is approx 3 cm and it is tennis ball.

• 1738/6368 = X/11
• 1738/6368*11= X
• 1738/6368*11 = 3.00219849246

I guessed ... I dunno this :(

6368 / 11 = 578.9 1738 / 578.9 = 2.99

Which rounds up to 3.

SF is the scale factor. (1738)SF=6368 We then divide 6368 by 1738 to find the SF to be around 3.66. n will be the radius of the object representing the moon. (n)SF=11. n=11/3.66. This equals 3 so the object should have a radius of around 3cm.

Divide 6368 by 1738. Divide the value of 11cm by the answer of the previous. Boom solution.

Very rough calculation:

$\frac{R_E}{R_M} = \frac{6300 km}{1700 km} \approx 3.7$

If $R_E \approx 11 cm$ , then $R_M \approx 3 cm$

• I solved it in a much faster way using estimation. Obviously the only issue here is one needs to have the multiple choice answers.

I used 6000km and 2000km to see that the ratio was roughly 3:1

Dividing 11 by 4 gives me 2.75 as a good estimate.

radius of the moon = (1738 x 11) / 6368 = 3.002

Calculate the difference between the radius between earth and which is 3.6 times then compare the options with the radius of football which one shows 3.6 that will be the ans..

All I did was take the earth's radius and divided it by the moon's radius and got an answer approximate to 3.

So it looked like this:

6368 ÷ 1738 = 3.663981588

Approx. 3 (Tennis Ball)

In any other math problem I would've rounded up to the nearest whole number.

But I rounded down. Why?

Well, the Tennis Ball was the closest object to the whole number 3.

It couldn't have been the Soft Ball because 3.6 (our answer) is closer to 3 (tennis ball) and not 4.5 (soft ball).

I tried to do it without a calculator. I turned all the fig to 2 sig. Fig. That is 6400 and 1700. Took the ration (6400/1700 is approximately 4). Then 4 x 2.75 be 11...the closest option was 3.

Just take the ratios. 63/17 is approx 3.6 so is 11/3

6368=1738 11 10^-5=x Cross multiply and we get x 6368=1738 11 10^-5 x=3.002 *10^-5km x=3.002 cm

I only read the title, then imagined Earth on my table and the moon next to it, and it came to me – it was definitely the size of a tennis ball; just using my hands to measure, remembering the sizes by heart. Nailed it. Then I read the full description and realized I had just bypassed a cumbersome calculation. LMAO

let x be the representation of moon... 636800/11 = 173800/x... x = approximately 3 cm as size radius of tennis ball ans..

Este es un problema de relación o escala, muy empleado en el dibujo de planos en ingeniería mecánica, civil, arquitectura y otras. En palabras se expresa: El radio de la tierra es al radio de la luna como el radio del modelo de la tierra es al radio del modelo de la luna. Matemáticamente: Rt/Rl = Rmt/Rml Numéricamente: 6378 km/1738 km = 11 cm/Rml La unidad km se cancela en la relación de la izquierda. Despejando la incognita: Rml = (1738/6368) * 11cm = 3.0022 cm Aproximadamente 3 cm esta es la respuesta. Tip 1: La matemáticas es un lenguaje como cualquiera y es importante hablar en matemáticas. Lo anterio es un ejemplo claro del uso del lenguaje de la matemática. Tip 2: El manejo de las unidades es muy importante. Observe que en este ejemplo no fue necesario convertir kilómetro (km) a centímetros (cm) porque la unidad km se anulo y la respuesta final está en cm y se debe mantener durante el desarrollo numérico del problema para evitar errores, además que ayuda a la solución, porque nos damos cuenta que el procedimiento fué correcto, al menos en ese sentido.

To find solutions to these problems , we can use the comparison between the actual radius with radius models. so the radius of the moon is a model ( 11x1738 ) : 6368 = 3.002 ... So, the best representation of the moon is tennis ball ( r = 3)

Without calculador... 6368 km is between 3 and 4 times bigger than 1738 km, near 4 times.

4 * 2 cm = 8 cm (too small)

4 * 4.5 cm = 18 cm (too big)

4 * 1 cm = 4 cm (too small)

4 * 3 cm = 12 cm (this is near 11 cm)

Followed the same principle as shown by Francis Nicole Raut of Philippines.

Let's consider the ratio of the radius of the Earth to that of the moon,

that's $\frac{6368}{1738}$

since we are given the radius of the ball to be $11$ , then the size of the object

representing the moon should be in the same ratio. Let the size of that object be

represented by $x$

comparing ratios we have,

$\frac{6368}{1738}$ = $\frac{11}{x}$ ,

making $x$ the subject, we have

$x$ = $\frac{11 \times 1738}{6368}$

    = 3

Taking a scale:

11cm:6368km, ? cm : 1738km, ?= (1738km x11cm)/6368km = 3.002198492= 3 cm (1 significant figure)

Since radius of earth and moon are given to be 6368and 1738Km, therefore 11/6368 = x/1738 that is 3 cm equovalent to tennis ball Ans

1738 x ( 3 ) = 5214 nearest number to 6368

3 x ( 3 ) = 9 nearest number to 11

so it's 3 XD

MoonRadius/EarthRadius = 0.2729 and 0.2729 * 11 nearly close to 3.0019