Question
<p>&lt;p&gt;The length of sides of a
square is twice the radius of a circle and perimeter of a rectangle is half the perimeter of the square. If the sum of length and breadth of rectangle is 16 cm, then find the area of the circle (in cm&lt;sup&gt;2&lt;/sup&gt;). [Take &amp;pi; = 2]&lt;/p&gt;</p>Solution
<p><p>Let the length of a square be &lsquo;a&rsquo;.</p> <p>And the radius of a circle be &lsquo;r&rsquo;.</p> <p>Now, a = 2r ----- (i)</p> <p>Perimeter of the rectangle = 1/2 &times; 4a = 2a</p> <p>=&gt; 2(l + b) = 2a</p> <p>=&gt; 2 &times; 16 = 2a</p> <p>=&gt; a = 16 cm</p> <p>Putting value of &lsquo;a&rsquo; in (i) we get,</p> <p>Radius = r = 16/2 = 8 cm</p> <p>Area of the circle = &pi;r<sup>2</sup>&nbsp;= 2 &times; 8 &times; 8 = 128 cm<sup>2</sup>.</p></p>
The question below is based on the given series I. The series I satisfy a certain pattern, follow the same pattern in series II and answer the questions...
97, 106, ?, 195, 411, 460
- What will come in place of the question mark (?) in the following series?
712, ?, 576, 508, 440, 372 - What will come in place of (?) in the given number series.
1, 8, 27, ?, 125, 216 24, 35, 57, 90, 134, ?
165      155     135     ?     65      15
...120, 157, 116, 159, ?, 165
What will come in place of the question mark (?) in the following series?
112, 116, 121, ?, 134, 142
32   48   96   ?   720   2520
What will come in place of the question mark (?) in the following series?
17, 81, 131, 169, 197, ?