Imagine you would have to put a rope around the moon. Since the moon is 1,738,000 metres in diameter, this is a hard task. Finally you have managed to get the rope around the moon but... it is one meter short.

You decide to dig a groove all around the moon, so that the shorter rope suffices. How deep must this groove be? (Assume the Moon to be a perfect sphere.)

man, you guys are creative with these problems. the circumference of the moon is (1,738,000*pi) meters, and the rope falls 1 meter short of this, so the circumference of the rope is [(1,738,000*pi)-1] meters. and the depth of the groove is the difference in the radiuses of the moon and the circle of the rope. so the radius of the rope is [(1,738,000*pi)-1]/2*pi meters which is approx = 868999.840 m...and the radius of the moon is 869000...so the groove must be 869000-868999.840 m approx. = 0.159154...meters; about 16 cm.

Posted by danny on 2002-11-12 17:42:33