11. In a school, students thought of planting trees in and around the school to reduce air
pollution. It was decided that the number of trees, that each section of each class will
plant, will be the same as the class, in which they are studying, e.g., a section of Class I
will plant 1 tree, a section of Class II will plant 2 trees and so on till Class XII. There are
three sections of each class. How many trees will be planted by the students?
12. A spiral is made up of successive
semicircles, with centres alternately at A
and B, starting with centre at A, of radii
0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, . . . as
shown in Figure. What is the total length
of such a spiral made up of thirteen
consecutive semicircles? (Take
22
7
p = )
[Hint : Length of successive semicircles is
l
1, l
2, l
3
, l4
, . . . with centres at A, B, A, B, . . ., respectively.]
13. 200 logs are stacked in the following manner: 20 logs in the bottom row, 19 in the next
row, 18 in the row next to it and so on. In how many rows are the 200 logs placed and
how many logs are in the top row?
14. In a bucket and ball race, a bucket is placed at the starting point, which is 5 m from the
first ball, and the other balls are placed 3 m apart in a straight line. There are ten balls in
the line.
A competitor starts from the bucket, picks up the nearest ball, runs back with it, drops it
in the bucket, runs back to pick up the next ball, runs to the bucket to drop it in, and she
continues in the same way until all the balls are in the bucket. What is the total distance
the competitor has to run?
[Hint : To pick up the first ball and the second ball, the total distance (in metres) run by
a competitor is 2 × 5 + 2 × (5 + 3)]
12. A spiral is made up of successive
semicircles, with centres alternately at A
and B, starting with centre at A, of radii
0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, . . . as
shown in Figure. What is the total length
of such a spiral made up of thirteen
consecutive semicircles? (Take
22
7
p = )
