Area, Perimeter, and Circumference Word Problems

A church is commissioning a circular stained glass window with a smaller circular design in its centre. The outer circle has a radius of 2.4 metres, while the inner circle has an area that is 1/9 of the total window area. What is the radius of the inner circle?

Answer explanation

Area of outer circle

= πr² = π(2.4)² = 18.1 m² (rounded to one dp)

Area of inner circle

=The inner circle's area is 1/9 of the total area

   =  18.1 ÷ 9 = 2.01 m²

use the area formula for a circle to find the radius of the inner circle:

   2.01 = πr²

   r² = 2.01 ÷ π

   r = √(2.01 ÷ π) ≈ 0.8 m

A farmer notices a mysterious crop circle in his field. It's composed of two circles: a larger outer circle and a smaller inner circle. The area between the two circles is 200 square metres. If the radius of the larger circle is 10 metres, what is the radius of the smaller circle?

Answer explanation

 Area between circles

= π(R² - r²) = 200

=  π(10² - r²) = 200

= 100π - πr² = 200

=  πr² = 100π - 200

= r² = 100 - 200/π ≈ 36.34

A new skateboard park is being designed in the shape of a trapezium. The parallel sides are 58m and 45m long, and the non-parallel sides are both 50m long. Inside the park, a circular area with a radius of 18 metres will be set aside for beginners. What percentage of the total park area is the beginners' circle?

Answer explanation

  Area of trapezium = 2575m²

  Area of circle = πr² = π × 16² =  804.2477 = 804.25m²

  Percentage = (804.25 ÷ 2575) × 100 = 31.233%

An artist is creating an installation using a square metal sheet. She cuts out a circle from the centre of the square. The area of the remaining metal (the square minus the circle) is 144cm². If the side length of the square is 14cm, what is the radius of the circular cut-out?

Answer explanation

Area of square = 14² = 196 cm²

  Area of circle =

πr² = 196 - 144  

     πr² = 52

     r² = 52 ÷ π ≈ 16.55

  Radius = 4.07 cm

Jojo bought a circular beach towel. The towel had a fringe around the entire edge of it. If the radius of the towel is 2.5 ft., how long was the fringe?

• 3.14

• 12.56

• 15.7

• 7.065

Jason is putting in a new circular shaped fire pit in his backyard. The diameter of the fire pit is 4 feet. What is the area of the backyard does the fire pit cover?

• 12.56

• 56.52

• 25.12

• 3.14

Juan is walking a circular track. The diameter of the track is 6 feet. If he walks 3 times around the track, how far does he walk?

• 18.84

• 56.52

• 200.96

• 15.7

Dewan has a circular island in his kitchen. The radius of the island is 1.5 feet. What area of the kitchen does the island cover?

• 7.065

• 15.7

• 25.12

• 9.42

Mark is putting a round fountain in his backyard. He decides to place bricks around the edge of the fountain. If the radius of the fountain is 1.5 feet, what is the length of the brick edge?

• 9.42

• 12.56

• 17.5

• 15.7

Joanne is making a cookie cake for her daughter's birthday. The diameter of the cookie is 16 inches. What is the area of the cookie?

• 200.96

• 354.34

• 56.52

• 37.68