Ivan has a circular garden with a diameter of 1.5 metres. He wishes to build a circular path around the garden with a width of 1 metre. How much area will the path cover?

Answer 1

#7.854\ m^2#

The radius #r_1# of the garden with a diameter #1.5\ m# is
#r_1=1.5/2=0.75\ m#
Since, the width of path around the circular garden is #1\ m# hence the outside radius #r_2# of garden with path around it
#r_2=0.75+1=1.75\ m#

hence, the area of path around the circular garden is

#=\pi(r_2^2-r_1^2)#
#=\pi(1.75^2-0.75^2)#
#=7.854\ m^2#
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Answer 2

To find the area of the path, subtract the area of the inner circle (garden) from the area of the outer circle (entire path).

  1. Calculate the radius of the inner circle (garden): Radius = Diameter / 2 Radius = 1.5 / 2 Radius = 0.75 meters

  2. Calculate the radius of the outer circle (entire path): Radius_outer = Radius_inner + Width Radius_outer = 0.75 + 1 Radius_outer = 1.75 meters

  3. Calculate the area of the inner circle (garden): Area_inner = π * Radius_inner^2 Area_inner = π * 0.75^2 Area_inner ≈ 1.77 square meters

  4. Calculate the area of the outer circle (entire path): Area_outer = π * Radius_outer^2 Area_outer = π * 1.75^2 Area_outer ≈ 9.62 square meters

  5. Calculate the area covered by the path: Area_path = Area_outer - Area_inner Area_path ≈ 9.62 - 1.77 Area_path ≈ 7.85 square meters

Therefore, the path will cover approximately 7.85 square meters.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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