Question

14. A circular flower garden has an area of 314 m². A sprinkler at the centre of the
garden can cover an area that has a radius of 12 m. Will the sprinkler water the entire
garden? (Take n=3.14)
​

Answer 1

Step-by-step explanation:

to find the radius of the circular garden

πr^2 = 314

3.14×r×r = 314

r×r = 314/3.14

r×r = 100

r = 10m

hence, the sprinkler will water the entire garden

Answer 2

Answer:

• Yes, the sprinkle can cover the whole garden.

Step-by-step explanation:

Given:

• Area of circular garden = 314 m²
• Radius of area covered by sprinkler = 12 m

To find:

• Will the sprinkler water the entire Garden?

We know that,

$\longrightarrow \bf Area\;of\;circular\;garden=\pi r^{2}\\ \\ \\ \longrightarrow \sf 314 = \dfrac{22}{7}\times r^{2}\\ \\ \\ \longrightarrow \sf 314\times 7=22r^{2}\\ \\ \\ \longrightarrow \sf 2198 =22r^{2}\\ \\ \\ \longrightarrow \sf r^{2}= \dfrac{2198}{22}\\ \\ \\ \longrightarrow \sf r^{2}=100\;m\\ \\ \\ \longrightarrow \sf r=\sqrt{100}\\ \\ \\ {\boxed{\longrightarrow {\bf r=10\;m}}}$

Hence, radius of garden = 10 m

And radius of area covered by sprinkler = 12 m.

∴ Yes, the sprinkle can cover the whole garden.

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