Shape and Space Solutions Week 2 Part 1

Step-by-Step Solutions: Area of Circles and Semicircles

Circles

For more examples of these questions and a deeper look, I recommend Amazon books: Level 1 (Grade 3/D level)

Level 2 (Grade 4/C Level)

1. Garden Pond

   • Question: A circular pond has a radius of 4 metres. What is the area of the pond?

     
     

   • Solution:

     • Formula for the area of a circle:

       
       

       Area = π × radius²

     • Substitute the radius (r = 4):

       
       

       Area = 3.14 × (4 × 4)

     • Calculate:

       
       

       Area = 3.14 × 16 = 50.24 m²

     • Final Answer: The area of the pond is 50.24 square metres.

       
       

2. Round Window

   • Question: A round window has a radius of 1.5 metres. Find the area of the window.

     
     

   • Solution:

     • Formula for the area of a circle:

       
       

       Area = π × radius²

     • Substitute the radius (r = 1.5):

       
       

       Area = 3.14 × (1.5 × 1.5)

     • Calculate:

       
       

       Area = 3.14 × 2.25 = 7.065 m²

     • Final Answer: The area of the window is 7.07 square metres (rounded to 2 decimal places).

       
       

Semicircles

1. Playground Sandpit

   • Question: A semi-circular sandpit has a radius of 2 metres. What is the area of the sandpit?

     
     

   • Solution:

     • First, find the area of the full circle:

       
       

       Area of Full Circle = π × radius²

     • Substitute the radius (r = 2):

       
       

       Area of Full Circle = 3.14 × (2 × 2) = 3.14 × 4 = 12.56 m²

     • Divide by 2 to find the area of the semicircle:

       
       

       Area of Semicircle = 12.56 ÷ 2 = 6.28 m²

     • Final Answer: The area of the sandpit is 6.28 square metres.

       
       

2. Decorative Arch

   • Question: A decorative semi-circular arch has a radius of 3 metres. Calculate the area of the arch.

     
     

   • Solution:

     • First, find the area of the full circle:

       
       

       Area of Full Circle = π × radius²

     • Substitute the radius (r = 3):

       
       

       Area of Full Circle = 3.14 × (3 × 3) = 3.14 × 9 = 28.26 m²

     • Divide by 2 to find the area of the semicircle:

       
       

       Area of Semicircle = 28.26 ÷ 2 = 14.13 m²

     • Final Answer: The area of the arch is 14.13 square metres.

       
       

Congratulations, how did you do? Let me know in the comments.

Without knowing it, by changing the formulas to numbers to solve these questions you have evaluated a formula, well done.