Case Study 2 A garden bed is shown below. It is a rectangle with semi-circular ends. It has a concrete circular fountain at the centre as shown. Grass is grown in the garden bed at all places except the central fountain region.
Answers
Complete Question :- Refer to image.
Solution :-
(i)
→ Diameter of concrete circular fountain = 14 m
So,
→ Radius = Diameter / 2 = 14/2 = 7 m
then,
→ Area of concrete circular fountain = πr² = (22/7) × 7 × 7 = 22 × 7 = 154 m² (c)
(ii)
→ Diameter of each semi-circular end = 14 m
So,
→ Radius = Diameter / 2 = 14/2 = 7 m
then,
→ Area of one semi-circular end = (1/2)πr² = (1/2) × (22/7) × 7 × 7 = 11 × 7 = 77 m² (d)
(iii)
→ Length of rectangle = 35 - (7 + 7) = 35 - 14 = 21 m
→ Breadth of rectangle = 14 m
So,
→ Area of rectangle = Length × Breadth = 21 × 14 = 294 m²
So,
→ Area of garden where grass is grown = (Area of rectangle - Area of concrete circular fountain) + 2•Area of one semi-circular end .
→ Required area = (294 - 154) + 2•77
→ Required area = 294 - 154 + 154
→ Required area = 294 m² (b)
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