| (i) A circular pond is surrounded by a 2 m wide circular path. if outer circumference of circular path is 44 m then the area of the path is P . |
| (ii) A rectangular courtyard measuring 17 m by \[9\frac{1}{2}\] is to be covered by square slabs, each of side \[\frac{1}{2}\]m. |
| Q slabs are required to cover the courtyard. |
| (iii) The minute hand of a circular clock is 15 cm long. The tip of the minute hand move R cm in 1 hour? |
A)
P Q R \[62.88\,{{m}^{2}}\] 348 100
B)
P Q R \[75.43\,{{m}^{2}}\] 646 \[94.2\]
C)
P Q R \[42.87\,{{m}^{2}}\] 200 44.5
D)
P Q R \[18.14\,{{m}^{2}}\] 544 79.4
Correct Answer: B
Solution :
Let rand R be the inner and outer radius of a circular pond respectively. Outer circumference of the path = 44 m i.e., \[2\pi R=44\] \[\Rightarrow \] \[2\times \frac{22}{7}\times R=44\,\,\Rightarrow \,\,R=7\,m\] Inner radius, \[r=(7-2)m=5\,m\] \[\therefore \] Area of the path \[=\pi {{R}^{2}}-\pi {{r}^{2}}\] \[=\pi ({{R}^{2}}-{{r}^{2}})=\frac{22}{7}({{7}^{2}}-{{5}^{2}})\] \[=\frac{22}{7}(49-25)=\frac{22}{7}\times 24=75.43{{m}^{2}}\] (ii) Length of courtyard = 17 m Breadth of courtyard \[=9\frac{1}{2}m=\frac{19}{2}\,m\] Area of courtyard = Length \[\times \] Breadth \[=17\times \frac{19}{2}=\frac{323}{2}{{m}^{2}}\] Side of each square slab \[=\frac{1}{2}\,m\] Area of one square slab \[={{(side)}^{2}}=\frac{1}{2}\times \frac{1}{2}=\frac{1}{4}\,{{m}^{2}}\] Required number of square slabs \[=\frac{Area\text{ }of\text{ }courtyard}{Area\text{ }of\text{ }one\text{ }slab~~~}=\frac{\frac{323}{2}}{\frac{1}{4}}=\frac{323}{2}\times 4=646\]1 (iii) Distance travelled by the tip of minute hand in 1 hour = Circumference of the clock\[=2\pi r=2\times 3.14\times 15=94.2\text{ }cm\]
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