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 inFig. 5.4. What is the total length of such a spiral made up of thirteen consecutive semicircles? (Take

[Hint : Length of successive semicircles is with centres at A, B, A, B, . . .,respectively.]

A sum of Rs 700 is to be used to give seven cash prizes to students of a school for theiroverall academic performance. If each prize is Rs 20 less than its preceding prize, find thevalue of each of the prizes.

In a school, students thought of planting trees in and around the school to reduce airpollution. It was decided that the number of trees, that each section of each class willplant, will be the same as the class, in which they are studying, e.g., a section of Class Iwill plant 1 tree, a section of Class II will plant 2 trees and so on till Class XII. There arethree sections of each class. How many trees will be planted by the students?

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 (see Fig. 5.5). In how may rows are the 200 logs placedand how many logs are in the top row?

In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato,and the other potatoes are placed 3 m apart in a straight line. There are ten potatoes in theline (see Fig. 5.6).

A competitor starts from the bucket, picks up the nearest potato, runs back with it, dropsit in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, andshe continues in the same way until all the potatoes are in the bucket. What is the totaldistance the competitor has to run?

[Hint : To pick up the first potato and the second potato, the total distance (in metres)run by a competitor is