Question

The diameter of the Moon is ______ of the earth.
A. \[\dfrac{1}{2}\]
B. \[\dfrac{1}{3}\]
C. \[\dfrac{1}{4}\]
D. \[\dfrac{2}{3}\]

Answer 1

Hint: This particular question is very easy but students need to know the diameters of moon as well as earth. We know that the diameter of earth is greater than the diameter of the moon. We can then take their ratio and get the final answer. We will then select the answer closest to our calculated ratio.

Complete step by step answer:
Since there seems to be no other easy way to answer this question, we must know the diameter of both entities. The diameter of the moon is 3474.2 km and that of earth is 12,742 km. Both of these diameters are approximate. Let's round up the diameter of the Moon as it would not affect our ratio considerably. So, we have 3474 km as the moon's diameter. Let's now take the ratio of diameter of moon to earth.
\[\dfrac{3474}{12742}=0.27\]
Now, we got the ratio as 0.27. So the closest answer to our ratio is \[\dfrac{1}{4}\]=0.25. All other ratios are unlikely to be the answer.

So, the correct answer is “Option C”.

Additional Information: Upon taking the ratio the answers do not match. So, in such cases we must always select the option closest to our derived answer. We have also used the approximation in values because of that too the answers may vary.

Note: This question can also be solved if we know the distance between earth and moon, the distance from circumference point of moon and earth’s diameter. By using this data we can create a right angle triangle with the right angle on moon and distance between moon’s circumference point and earth as the hypotenuse. Then we can find the radius of the moon using hypotenuse. After that we can take a ratio of their radius as our answer. Bit this whole method would be too tedious. It's better and always useful to know the diameters of earth and moon.