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(D) The side of the square is $a = 21 \, m$.Area of the square $= a^{2} = 21 	imes 21 = 441 \, m^{2}$.There are four semi-circles on the four sides o

Vedclass · Accepted Answer

$189$

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(D) The side of the square is $a = 21 \, m$.Area of the square $= a^{2} = 21 	imes 21 = 441 \, m^{2}$.There are four semi-circles on the four sides of the square. The diameter of each semi-circle is equal to the side of the square,which is $21 \, m$.Therefore,the radius of each semi-circle is $r = \frac{21}{2} = 10.5 \, m$.Area of four semi-circles $= 4 	imes (\frac{1}{2} 	imes \pi 	imes r^{2}) = 2 	imes \pi 	imes r^{2}$.Area $= 2 	imes \frac{22}{7} 	imes 10.5 	imes 10.5 = 2 	imes \frac{22}{7} 	imes \frac{21}{2} 	imes \frac{21}{2} = 22 	imes 3 	imes 10.5 = 693 \, m^{2}$.Total area of the bed $= 441 + 693 = 1134 \, m^{2}$.Given that each rose plant needs $6 \, m^{2}$ of space.Number of plants $= \frac{	ext{Total Area}}{	ext{Area per plant}} = \frac{1134}{6} = 189$.

$A$ bed of roses is shaped as shown in the figure below. In the centre is a square and on each side there is a semi-circle. The side of the square is $21 \, m$. If each rose plant needs $6 \, m^{2}$ of space,then the number of plants in the bed is?

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