High School

Given a circle with circumference 157 cm. Prove that the radius of this circle is approximately 25 cm.

We know that the circumference of a circle is given by the formula: C = 2 × π × r, where C is the circumference and r is the radius.

Given C = 157 cm, we can solve for r:

157 = 2 × π × r

r = 157 / (2π)

Using π ≈ 3.14, we get:

r ≈ 157 / (2 × 3.14)

r ≈ 157 / 6.28

r ≈ 25 cm.

Answer :

To determine the radius of a circle given its circumference, we use the formula for the circumference of a circle:

[tex]C = 2 \times \pi \times r[/tex]

Where:

  • [tex]C[/tex] is the circumference,
  • [tex]\pi[/tex] is a mathematical constant approximately equal to 3.14,
  • [tex]r[/tex] is the radius we need to find.

In this problem, we are given:
[tex]C = 157 \, \text{cm}[/tex]

To find the radius [tex]r[/tex], we need to rearrange the formula:

[tex]r = \frac{C}{2 \times \pi}[/tex]

Substitute the given value of [tex]C[/tex] and the approximate value of [tex]\pi[/tex] into the equation:

[tex]r = \frac{157}{2 \times 3.14}[/tex]

Calculate the denominator:

[tex]2 \times 3.14 = 6.28[/tex]

Now, divide the circumference by this value:

[tex]r = \frac{157}{6.28} \approx 25 \, \text{cm}[/tex]

Thus, the radius of the circle is approximately 25 cm.

Other Questions