CBSE Class 10 Maths (Basic) 2024 · Paper 430/1/1 · Question 36

Quadratic Equations 4 marks Medium

To keep the lawn green and cool, Sadhna uses water sprinklers which rotate in circular shape and cover a particular area. The diagram shows the circular areas covered by two sprinklers of radii

R

and

r

(

R > r

). Two circles touch externally. The sum of their areas is

130 π

sq m and the distance between their centres is

14

m. Based on the above information, answer the following questions.

Two externally touching circles of radii R and r (R > r)

(i)Obtain a quadratic equation involving $R$ and $r$ from above.[1]
(ii)Write a quadratic equation involving only $r$ .[1]
(iii)(a)Find the radius $r$ and the corresponding area irrigated.[2]
(iii)(b)OR Find the radius $R$ and the corresponding area irrigated.[2]

Answer

(i)

R^{2} + r^{2} = 130

(from

π R^{2} + π r^{2} = 130 π

); (ii)

r^{2} - 14 r + 33 = 0

; (iii)(a)

r = 3

m, area irrigated

= 9 π

sq m

\approx 28.29

sq m; (iii)(b)

R = 11

m, area irrigated

= 121 π

sq m

\approx 380.29

sq m (taking

π = \frac{22}{7}

🔒 Step-by-step solution

From the board paper

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CBSE Class 10 Maths (Basic) 2024 · Paper 430/1/1 · Question 36

Answer

From the board paper

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