Question

b) the diameter of a circle with area 1256 cm²
f) image of a square with side 8.5 cm and an inscribed circle with radius 2.5 cm (or diameter related?)

Explanation:

Step1: Recall the area formula of a circle

The area formula of a circle is \( A=\pi r^{2} \), where \( A \) is the area and \( r \) is the radius. We know \( A = 1256\space cm^{2}\) and take \( \pi\approx3.14\). So we can solve for \( r \) first.
Substitute the values into the formula: \( 1256 = 3.14\times r^{2}\)

Step2: Solve for the radius \( r \)

First, divide both sides of the equation by \( 3.14 \): \( r^{2}=\frac{1256}{3.14}=400\)
Then, take the square root of both sides: \( r=\sqrt{400} = 20\space cm\)

Step3: Calculate the diameter \( d \)

The diameter of a circle is related to the radius by the formula \( d = 2r \). Substitute \( r = 20\space cm\) into the formula: \( d=2\times20 = 40\space cm\)

Answer:

The diameter of the circle is \( 40\space cm \)