Question

the diameter of a planet is approximately one sixth of the diameter of the earth find the ratio of their surface areas​

Answer 1

Answer:

1:3

Step-by-step explanation:

Assuming earth's diameter to be x ,

Surface area of earth = 4 × pi × r×r

= 4 × pi × x/2 × x/2

= 4× pi × x^2/4

Surface area of planet= 4 × pi × (x/6)/2 × (x/6)/2

= 4 x pi x (x^2/6)×1/2

= 4 x pi × x^2/12

Ratio = (4×pi×x^2/4) / 4×pi×x^2/12

= 1:3

Answer 2

Answer:

The ratio of the surface area of earth and planet ​ is 36:1

Step-by-step explanation:

• The shape of the planets is a sphere.
• The surface area of a sphere is $4\pi r^{2}$ , where r is the radius of the sphere.

Step 1 of 2:

• Let the diameter of the earth is x.
• The radius of the earth is $\frac{x}{2}$.
• The diameter of the planet is  $\frac{x}{6}$
• The radius of the planet is  $\frac{x}{12}$
• The surface area of the earth is $4\pi r^{2}$

      $SA \ earth=4\pi r^{2}$

       $SA \ earth=4\pi (\frac{x}{2}) ^{2}\\\\SA \ earth= \pi x^{2}$

• The surface area of the planet is $4\pi r^{2}$
•      
• $SA \ planet=4\pi r^{2}$
•      
• $SA \ planet=4\pi( \frac{x}{12}) ^{2}\\\\SA \ planet=\pi \frac{x^2}{36}$

Step 2 of 2:

• The ratio of their surface areas​ is

           $\frac{SA \ earth}{SA \ planet} =\frac{\pi x^{2}}{\pi \frac{x^{2}}{36} } \\\frac{SA \ earth}{SA \ planet}=36:1$