Find the area of the flower bed (with semi-circular ends) shown in Fig. 11.6
Solution:
Given, flower bed with semicircular ends.
We have to find the area of the flower bed.
From the figure,
ACDF is a rectangular bed with semicircular ends.
Length of the rectangular bed = 38 cm
Breadth of the rectangular bed = 10 cm
Area of rectangle = length × breadth
Area of rectangular bed = 38 × 10
= 380 cm²
Area of semicircle = πr²/2
Breadth of rectangular bed = diameter of semicircular end
Diameter of semicircular end = CA = DF = 10 cm
Radius = 10/2 = 5 cm
So, area of semicircular end = π(5)²/2
= 25π/2 cm²
Since there are two semicircular ends,
Area of semicircular ends = 2(25π/2)
= 25(22/7)
= 78.572 cm²
Area of flower bed = area of rectangular bed + area of semicircular ends
= 380 + 78.572
= 458.572 cm²
Therefore, the area of the flower bed is 458.572 cm².
✦ Try This: A rectangular park is 100m by 50 m. It is surrounded by semi-circular flower bed all round. Find the cost of leveling the semi-circular flower bed sall 60 paise per square meter.
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 12
NCERT Exemplar Class 10 Maths Exercise 11.3 Problem 6
Find the area of the flower bed (with semi-circular ends) shown in Fig. 11.6
Summary:
Area is the quantity that measures the number of unit squares that cover the surface of a closed figure. The area of the flower bed with semicircular beds is 458.572 cm²
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