Square Side Length Calculation
The area of the square is provided as \(196 \text{ cm}^2\). The area of a square is calculated using the formula \(A = s^2\), where \(s\) is the side length.
We set up the equation:
\(s^2 = 196 \text{ cm}^2\)
Taking the square root of both sides gives the side length:
\(s = \sqrt{196} \text{ cm} = 14 \text{ cm}\)
Circle Radius Calculation
The problem states that the side length of the square (\(s\)) is equal to the diameter (\(d\)) of the circle.
So, the diameter of the circle is:
\(d = s = 14 \text{ cm}\)
The radius (\(r\)) of the circle is half of its diameter:
\(r = \frac{d}{2} = \frac{14 \text{ cm}}{2} = 7 \text{ cm}\)
Circle Area Calculation
The area of a circle is given by the formula \(A = \pi r^2\). We are instructed to use \(\pi = \frac{22}{7}\).
Substitute the radius and the value of \(\pi\) into the formula:
Area \(= \frac{22}{7} \times (7 \text{ cm})^2\)
Area \(= \frac{22}{7} \times 49 \text{ cm}^2\)
Simplify the calculation:
Area \(= 22 \times 7 \text{ cm}^2 = 154 \text{ cm}^2\)
The area of the circle is \(154 \text{ cm}^2\). This corresponds to Option A.
Similar Questions
- What is the area of a square whose diagonal measures 4 cm?
- Calculate the length of the diagonal of a square if the area of the square is 32 cm\(^2\).
- A farmer wants to fence his rectangular field of length 200 m and area 3000 \(\text{m}^2\). If the cost of fencing per metre is 5 rupees, what is the total cost of fencing in rupees?
The inner and outer diameters of ring 1 of a dartboard are 15 cm and 17 cm respectively and those of ring II are 12 cm and 13 cm respectively. What is the total area of these two rings?
- A car has two wipers which do not overlap. Each wiper has a blade of length 18 cm sweeping through an angle of \(126^\circ\). Find the total area cleaned at each sweep of the blades. Take \(\pi = 22/7\)
\(ABCD\) is a diameter of a circle of radius 12 cm. The lengths \(AB\), \(BC\) and \(CD\) are equal. Semi-circles are drawn on \(AB\) and \(BD\) as diameters as shown in the given figure. Find area of the shaded region.
- What is the area in sq. cm. of the triangle with a base of 8 cm and sides of length 6 cm each?
- The length of a board is 12 cm and its breadth is 3 cm. The board needs to be taped around its sides covering all four sides. How long the tape should be?
- What is the area of the parallelogram whose base is \(5\text{ cm}\) and corresponding height is \(6\text{ cm}\)?
Important Questions from 2-D Mensuration
- The length of a rectangular plot is $(x^2 + xy + y^2)$ m and its breadth is $(x^2 - 5xy - y^2)$ m.
Find its perimeter, when $x = 1$ and $y = -1$. - The ratio between the perimeter and breadth of a rectangle is 3: 1. If the area of the rectangle is $98 \text{ cm}^2$, find the perimeter (in cm) of the rectangle.
The shorter side of a rectangle is 15 cm less than the longer side. The numerical value of its area is equal to 5 times the numerical value of its perimeter. What is the length (in cm) of its longer side?
- In a circle of radius 10.5 cm, if the angle of a sector is $\frac{2\pi}{3}$, then the perimeter of the sector is (in cm):
(Take $\pi = \frac{22}{7}$) - Find the circumference (in m) of the largest circle that can be inscribed in a rectangle whose dimensions are given as 114 m and 63 m.
Take $\pi = \frac{22}{7}$
