Step 1: Formula for Area of a Circle.
The area of a circle is calculated by the formula: \[ \text{Area} = \pi \times \text{radius}^2 \] For a circle with a radius of 7 cm, the area will be: \[ \text{Area} = \pi \times 7^2 = 7 \times 7\pi \] Step 2: Verifying the Options.
- Option (1): \( 7\pi \) is incorrect, as the area formula involves squaring the radius.
- Option (2): \( 7 \times 7\pi \) is correct.
- Option (3): \( 7 \times 7 \times 7\pi \) is incorrect.
- Option (4): \( 7 \times 7 \times 7 \times 7\pi \) is incorrect.
Conclusion:
Therefore, the correct answer is (2) \( 7 \times 7\pi \).
Find the number of triangles in the given figure.
Find the unknown frequency if 24 is the median of the following frequency distribution:
\[\begin{array}{|c|c|c|c|c|c|} \hline \text{Class-interval} & 0-10 & 10-20 & 20-30 & 30-40 & 40-50 \\ \hline \text{Frequency} & 5 & 25 & 25 & \text{$p$} & 7 \\ \hline \end{array}\]
Two concentric circles are of radii $8\ \text{cm}$ and $5\ \text{cm}$. Find the length of the chord of the larger circle which touches (is tangent to) the smaller circle.