Question 7: The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas.

online.maxtute.com

**Given Data**: The diameter of the moon is approximately one fourth the diameter of the earth.

Because radius is half the diameter, the radius of the moon is also approximately one fourth the radius of the earth.

Let the radius of the earth be r_{1}.

Let the radius of the moon be r_{2}.

Radius of the moon, r_{2} = \\frac{1}{4}) x r_{1}

or r_{1} = 4r_{2} ……(1)

Surface area of moon = 4 × π × r_{2}^{2}

Surface area of earth = 4 × π × r_{1}^{2}

Ratio of their surface areas = \\frac{\text{Surface Area of Moon}}{\text{Surface Area of Earth}})

= \\frac{4 × π × r_2^2}{4 × π × r_1^2})

= \\frac{r_2^2}{ r_1^2})

= \\frac{r_2^2}{(4 r_2)^2})

= \\frac{1}{16})

**Ratio of surface areas of the moon and the earth = 1 : 16**

Class 9 Maths

Register in 2 easy steps and

Start learning in 5 minutes!

Copyrights © 2016 - 22 All Rights Reserved by Maxtute.com - An Ascent Education Initiative.

Privacy Policy | Terms & Conditions

**Phone:** (91) 44 4500 8484

**Mobile:** (91) 93822 48484

**WhatsApp:** WhatsApp Now

**Email:** learn@maxtute.com