A circular pool with a radius of r metres is surrounded by a circular path 1.5 metres wide.
a) find the expression for the area of the pool?
b) find,interms of r the distance from the centre of the pool to the outer edge of the path?
C) find the area of the circle that includes the path and the pool.(do not expand the expression)
D) write a simplified expression for the area of the path?
E)if the pool had a radius of 5 metres, what would be the area of the path to the nearest square metres?
F)if the pool had a radius of 7 metres, what would be the area of the circle that includes the path and the pool?
Answers
Solution :-
Length of the path = 1.5m
Radius of pool = r
Radius of outer circle = R = (1.5 + r)m
a.) Area of the pool = πr²
b.) The distance from the centre of the pool to the outer edge of the path = R = (1.5 + r)m
c.) Area of the circle that includes the path and the pool is the area of outer circle.
Area of outer circle
= π × R²
= π × (1.5 + r)² m²
d.) Area of the path
= Area of the outer - Area of inner circle
= π × (1.5 + r)² m² - π × r²m²
e.) Radius of pool (r) = 5m
Area of the path
= π × (1.5 + r)² m² - π × r²
= π × (1.5 + 5)² m² - π × (5m)²
= π × (6.5)² m² - π × 25m²
= π × 42.25 m² - π × 25 m²
= π × (42.25 - 25)m²
= π × 17.25m²
Taking π as 3.14
= 3.14 × 17.25m²
= 54.165 m²
f.) Radius of pool (r) = 7m
Radius of outer circle (R) = 1.5 + r = 1.5 + 7m = 8.5m
Area of outer circle
= π × R²
= π × (8.5)² m²
= π × (72.25) m²
Taking π as 3.14
= 3.14 × 72.25 m²
= 226.865 m²
Diagram is in the attachment.
