9765
/www/nrich/html/content/id/9765/
1
2013-01-04T16:09:36
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0">A snail is at one corner of the top face of a cube with side length $1$m. The snail can crawl at a speed of $1$m per hour. What proportion of the cube's surface is made up of points which the snail could reach within one hour?</mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0">In one hour, the snail can reach points within $1$m of the corner at which it starts. So it can reach some of the points on the three faces which meet at that corner, but none of the points on the other three faces.<br></br>
<br></br>
On each of the reachable faces, the oints which the snail can reach form a quarter of a circle of radius $1$m. So the required fraction is $\frac{\pi}{8}$.</mdoxml>
2
3
0
0
1
0
0
Weekly Problem 6 - 2013
Weekly Problem 6 - 2013