In front of the School entrance gate there is a flag with a circular garden beneath it. The students of
grade IX decided that this circular garden would be their community service project. The students
elected Riya the leader of the project and she got right to work organizing the decorating. She asked
for a group of students to plant flowers and rake the leaves left from last autumn. It was a perfect
spring project
"We need more dirt," Rohan said soon after the clean-up had begun.
"I think so too," said Arpita.
Riya went out to assess the situation. The rain and snow of the winter and early spring had left the
ground sparse. There definitely was not enough dirt to plant in. Riya began to figure out the area of
the circular garden.
She knew that the formula for area is A = πr^2. The diameter of the garden is 16 feet.
What do you think is the area of the circular garden?
Define the value. Is it a rational or irrational number? Explain.
Assuming π=22/7, for what value of radius do you think the value will be a natural number?
Find your answer in sq.m.
Answers
Given : . The diameter of the garden is 16 feet.
π=22/7
To Find : area of the circular garden
Is it a rational or irrational number
value of radius for which the area will be a natural number
Solution:
Rational numbers p/q where p and q are integers and q ≠ 0
π=22/7 Hence rational number
Diameter = 16 ft
=> Radius = Diameter /2 = 16/2 = 8 ft
Area = π (radius)²
=> area = (22/7) * ( 8)² = 1408/7 ft²
this is also rational number
for natural numbers q = 1
Hence radius must be of form 7k
like 7 , 14 , 21 and so on for area to be natural number
for example radius = 7 ft
=> Area = (22/7)* 7² = 154 ft²
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