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Harrizon [31]
3 years ago
14

You are placing non-slip tape along the perimeter of the bottom of a semicircle-shaped doormat. How much tape will you save appl

ying the tape to the perimeter of the inside semicircle of the doormat? Round your answer to the nearest hundredth, if necessary. A semicircle-shaped doormat with diameter of 30 inches. A 3 inches wide non-slip tape is placed along the perimeter of the bottom of the doormat.
Mathematics
1 answer:
sdas [7]3 years ago
5 0

Answer:

The amount of tape to be saved is 15.43 inches.

Step-by-step explanation:

Semicircle is half of a given circle, consisting of an arc and a diameter. Its perimeter is determined by adding the length of its arc to the diameter.

perimeter of a semicircle = length of its arc + its diameter

length of the arc = half of the circumference of its circle

circumference of a circle = 2\pir

half of the circumference of a circle = \pir

length of the arc of the semicircle = half of the circumference of a circle = \pir

The initial diameter of the semicircle = 30 inches

⇒ its radius, r = 15 inches

Amount of tape to be saved = Initial perimeter of the semicircle - perimeter of the inside of the semicircle

Initial perimeter of the semicircle = \pir + length of the diameter

                                                       =  \frac{22}{7} × 15 + 30

                                                       = 47.1429 + 30

                                                       = 77.1429 inches

Initial perimeter of the semicircle is 77.1429 inches.

The inside semicircle is formed, since a tape of width 3 inches has been placed along the perimeter of the initial doormat. Then,

diameter of the inside semicircle = 30 - 6

                                               = 24 inches

⇒           its radius = 12 inches

perimeter of the inside semicircle = \pir + length of the diameter

                                                        =  \frac{22}{7} × 12 + 24

                                                        = 37.7143 + 24

                                                       = 61.7143 inches

perimeter of the inside semicircle is 61.7143 inches.

Amount of tape to be saved = 77.1429 - 61.7143

                                               = 15.4286

The amount of tape to be saved is 15.43 inches.

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