CBSE Class 10 Maths (Basic) 2025 · Paper 430/1/1 · Question 37

Arithmetic Progressions 4 marks Medium

In a garden, saplings of rose flowers were planted at equal intervals to form a spiral pattern. The spiral is made up of successive semicircles, with centres alternatively at A and B, starting with centre at A, of radii 50 cm, 100 cm, 150 cm, ... as shown in the figure given below. Spiral 1 has 10 flowers, Spiral 2 has 20 flowers, Spiral 3 has 30 flowers and so on. Based on the above information, answer the following questions :

Spiral of semicircles with centres alternately at A and B; consecutive radii labelled l1, l2, l3, l4.

iWhat is the radius of the 13th spiral?[1]
iiIf the radius of the nth spiral is 500 cm, find the value of $n$ .[1]
iii (a)Find the total number of saplings till the 11th spiral.[2]
iii (b)Till which spiral, will there be a total of 450 saplings?[2]

Answer

(i) The radius of the 13th spiral is

650

cm; (ii)

n = 10

; (iii)(a) The total number of saplings till the 11th spiral is

660

; (iii)(b) There will be a total of

450

saplings till the 9th spiral.

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CBSE Class 10 Maths (Basic) 2025 · Paper 430/1/1 · Question 37

Answer

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