Question

find the diagonal of the given figure.
circle
area = 616 sq. cm
14 cm
7 cm
28 cm
88 cm

Explanation:

Step1: Recall the formula for the area of a circle

The area of a circle is given by \( A = \pi r^2 \), where \( A \) is the area and \( r \) is the radius. We know the area \( A = 616 \) sq. cm and \( \pi=\frac{22}{7} \). So we set up the equation:
\( 616=\frac{22}{7}\times r^2 \)

Step2: Solve for \( r^2 \)

First, multiply both sides by \( \frac{7}{22} \):
\( r^2 = 616\times\frac{7}{22} \)
Calculate \( 616\div22 = 28 \), then \( 28\times7 = 196 \). So \( r^2 = 196 \), which means \( r = 14 \) cm (since radius is positive).

Step3: Find the diameter of the circle

The diameter \( d \) of a circle is \( d = 2r \). Substituting \( r = 14 \) cm, we get \( d = 2\times14 = 28 \) cm.

Step4: Relate the diagonal of the square to the diameter of the circle

In the given figure, the square is inscribed in the circle, so the diagonal of the square is equal to the diameter of the circle. Therefore, the diagonal of the square (the given figure's diagonal we need to find) is equal to the diameter of the circle, which is 28 cm.

Answer:

28 cm