# Practice Questions on Geometry & MensurationAptitude Questions and Answers

## Difficult Geometry & Mensuration Question - 6

 Q6. $\triangle ABC$ is an equilateral triangle of side 14 cm. A semi circle on $BC$ as diameter is drawn to meet $AB$ at $D$,  and $AC$ at $E$. Find the area of the shaded region.
 A. $49\left(\dfrac{\pi}{3}-\sqrt{3}\right)\text{ cm}^2$ B. $49\left(\dfrac{\pi}{3}-\dfrac{\sqrt{3}}{2}\right)\text{ cm}^2$ C. $49\text{ cm}^2$ D. None

## Difficult Geometry & Mensuration Question - 7

 Q7. Through $T$, the mid-point of the side $QR$ of a  $\triangle PQR$ , a straight line is drawn to meet $PQ$ produced to $S$ and $PR$ at $U$, so that $PU = PS$. If length of $UR = 2$ units then the length of $QS$ is
 A. $2\sqrt{2}$ units B. $\sqrt{2}$ units C. $2$units D. cannot be determined

## Difficult Geometry & Mensuration Question - 8

 Q8. A sphere of radius $r$ is cut by a plane at a distance of $h$ from its center, thereby breaking this sphere into two different pieces. The cumulative surface area of these two pieces is 25% more than that of the sphere.  What is the value of $h$?
 A. $\dfrac{r}{\sqrt{2}}$ B. $\dfrac{r}{\sqrt{5}}$ C. $\dfrac{r}{\sqrt{7}}$ D. $\dfrac{r}{\sqrt{11}}$

## Difficult Geometry & Mensuration Question - 9

 Q9. Two mutually perpendicular chords $AB$ and $CD$ meet at a point $P$ inside the circle such that $AP = 6$ cms, $PB = 4$ units and $DP = 3$ units.  What is the area of the circle?
 A. $\dfrac{125\pi}{4}$ sq cms B. $\dfrac{100\pi}{7}$ sq cms C. $\dfrac{125\pi}{8}$ sq cms D. $\dfrac{52\pi}{3}$ sq cms

## Difficult Geometry & Mensuration Question - 10

 Q10. The figure below shows two concentric circle with centre O. PQRS a square, inscribed in the outer circle. It also circumscribes the inner circle, touching it at points B, C, D and A. What is the ratio of the perimeter of the outer circle to that of polygon ABCD?
 A. $\pi / 4$ B. $3 \pi / 2$ C. $\pi / 2$ D. $\pi$
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