Calculation of pool diameter: solving an interesting mathematical problem

Want to know the diameter of the swimming pool? Let's solve an interesting math problem first! Through this problem, we can understand the area formula of the ring and the relationship between the radius of the big circle and the radius of the small circle. Next, we will use this information to calculate the diameter of the pool.

Annular area formula

The area formula of the ring is: πR? -πr？ =π（R？ -r？ )。 Where r is the radius of the big circle and r is the radius of the small circle.

Relationship between radius of big circle and radius of small circle

There is a magical relationship between the radius r of the great circle and the radius r of the small circle: R=r+ 1.5.

Calculate π(R? -r？ The value of)

By replacing the relationship between R and R, we get π [(r+1.5)? -r？ ]。 Further simplification, we get π [r? +3r+2.25-r？ 】, which is π [3r+2.25].

Solve the equation and find the value of R.

The title tells us that π [3r+2.25] = 40.035. Solving this equation, we get 3r+2.25= 12.75. Further solution is 3r= 10.5, and finally r=3.5.

Calculate the pool diameter

According to the value of R, we can calculate that the diameter of the pool is 3.5× 2 = 7m.