Problems of the Week June 10 to June 14

Lower Elementary:

Question: The Moon is 3500 kilometres wide. The Earth is 12 700 kilometres wide. How many kilometres wider is the Earth than the Moon?

Answer:  9200 kilometres

Solution:  To solve the problem, we want to set up a vertical equation, start at the ones place, and move left. We know that 0 – 0 = 0, so we can fill in the ones and tens places and move on to the hundreds. 7 hundred minus 5 hundred is 2 hundred, and 12 thousand minus 3 thousand is 9 thousand. Altogether, that makes 9200 km.

Upper Elementary:

Question: For every 2 revolutions Pluto makes around the Sun, Neptune makes 3. How many revolutions does Pluto complete if Neptune completes 21?

Answer:  14 revolutions

Solution:  The ratio of Pluto’s revolutions to Neptune’s revolutions is 2:3. To find out how many revolutions Pluto completes, we first need to find out how many times Neptune makes 3 trips. 21 ÷ 3 = 7, so Neptune make 7 sets of 3 revolutions. That means that Pluto makes 7 sets of 2 revolutions, which means that Pluto revolves around the sun 7 × 2 = 14 times.

Middle School:

Question: Callisto, Europa, Ganymede, and Io are moons of Jupiter. Ganymede is not the farthest moon from Jupiter. Callisto’s orbit is not the closest orbit to Io’s. Europa is closer to Jupiter than Ganymede is. Io is the closest to Jupiter. What is Jupiter’s farthest moon?

Answer:  Callisto

Solution:  Right off the bat, we know that Io is the closest and Ganymede is not the farthest. Next, we can deduce that Europa is the second closest because that’s the only possible way for it to be closer to Jupiter than Ganymede, which must therefore be third. That leaves Callisto, which must therefore be the farthest. Tip: Use a logic table to keep track of the information.

Algebra and Up:

Question: Mars has a radius of 3000 kilometres. Venus has a radius of 6000 kilometres. How many cubic kilometres greater is the volume of Venus than the volume of Mars? Give your answer in terms of pi.

Answer:  252 000 000 000 π  km³  or  2.52 × 10¹¹ π  km³

Solution:  We use the formula ⁴/₃πr3 to find the volume of each planet. Venus’s volume is 288 000 000 000π km³, and Mars’s volume is 36 000 000 000π km³. The difference is therefore 252 000 000 000π km³.