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Q 1. In the following figure {tex}\mathrm{BOD}{/tex} is the arc of a circle with centre C having radius {tex} 2 \mathrm { cm } {/tex}. {tex}\mathrm{ABCD}{/tex} is a square and {tex} \Delta \mathrm { CEF } {/tex} is an isosceles right-angled triangle whose equal sides are {tex} 6 \mathrm { cm } {/tex} long. Find the area of the shaded
region.
{tex} 2.02 \mathrm { cm } ^ { 2 } {/tex}
{tex} 7.07 \mathrm { cm } ^ { 2 } {/tex}
{tex} 21.14 \mathrm { cm } ^ { 2 } {/tex}
{tex} 14.04 \mathrm { cm } ^ { 2 } {/tex}
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Q 2. In the figure as mentioned below, {tex}\mathrm{POQ}{/tex} and {tex}\mathrm{ROS}{/tex} are diameters of a circle with centre {tex}\mathrm{O}{/tex} and radius {tex} 14 \mathrm { cm } . {/tex}
Find the area of the shaded region. (Take {tex}\pi = \frac { 22 } { 7 } {/tex})
{tex} 154 \mathrm { cm } ^ { 2 } {/tex}
{tex} 112 \mathrm { cm } ^ { 2 } {/tex}
{tex} 266 \mathrm { cm } ^ { 2 } {/tex}
{tex} 308 \mathrm { cm } ^ { 2 } {/tex}
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Q 3. Two circles touch internally and their centres are {tex} \mathrm { O } {/tex} and {tex} \mathrm { O } ^ { \prime } {/tex}. The difference of their areas is {tex}\mathrm{264 sq.}{/tex} {tex} \mathrm { cm } . {/tex} and the distance between their centres is {tex} 6 \mathrm { cm } . {/tex} What is the diameter of the larger circle?
{tex} 16 \mathrm { cm } {/tex}
{tex} 10 \mathrm { cm } {/tex}
{tex} 18 \mathrm { cm } {/tex}
{tex} 4 \mathrm { cm } {/tex}
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Q 4. The figure shows nine {tex} 1 \mathrm { cm } \times 1 \mathrm { cm } {/tex} squares and a circle. The circle passes through the centres of the squares in the four corners. Find the area of shaded region.
{tex} 81 - \sqrt { 2 } \pi {/tex}
{tex} \frac { 9 - 2 \pi } { 4 } {/tex}
{tex} 9 - 2 \pi {/tex}
{tex} \frac { 81 - 2 \pi } { 2 } {/tex}
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Q 5. A circle is inscribed in an isosceles trapezium {tex}\mathrm{ABCD}{/tex} in which {tex}\mathrm{AB}{/tex} is parallel to {tex}\mathrm{DC}{/tex}. If {tex}\mathrm{AB}=10{/tex} and {tex} \mathrm { DC } = 30 . {/tex} Find the area of the circle.
{tex} 40 \pi {/tex}
{tex} 50 \pi {/tex}
{tex} 60 \pi {/tex}
{tex} 75 \pi {/tex}