Calculating Circle Diameter from Area
The problem asks for the diameter of a circle given its area (\(A = 154\text{ cm}^2\)) and the value of pi (\(\pi = 22/7\)). We can find the diameter using the circle's area formula.
Circle Area Formula
The formula for the area of a circle is given by:
\(A = \pi r^2\)
where \(A\) is the area and \(r\) is the radius.
Finding the Radius
Substitute the given values into the formula:
\(154 = \frac{22}{7} \times r^2\)
To find \(r^2\), rearrange the equation:
\(r^2 = 154 \times \frac{7}{22}\)
Calculate the value:
\(r^2 = \frac{154}{22} \times 7\)
\(r^2 = 7 \times 7\)
\(r^2 = 49\)
Now, find the radius by taking the square root:
\(r = \sqrt{49}\)
\(r = 7\text{ cm}\)
Calculating the Diameter
The diameter (d) of a circle is twice its radius (r):
\(d = 2r\)
Substitute the calculated radius:
\(d = 2 \times 7\text{ cm}\)
\(d = 14\text{ cm}\)
Conclusion
The diameter of the circle is 14 cm. This matches the first option.
Important Questions from Circles
If 3x + y - 5 = 0 is the equation of a chord of the circle x2 + y2 - 25 = 0, then what are the coordinates of the mid-point of the chord ?
What is the area of minor segment ?
What is the area of major segment ?
A straight line x = y + 2 touches the circle 4(x 2+ y 2) = r 2. The value of r is
If the centre of the circle passing through the origin is (3, 4), then the intercepts cut off by the circle on x-axis and y-axis respectively are
