Practice Questions on Geometry & Mensuration
Aptitude 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.

Image for Geometry and Mensuration, Aptitude:2189-1

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

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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

Image for Geometry and Mensuration, Aptitude:2190-1

A.

\(2\sqrt{2}\) units

B.

\(\sqrt{2}\) units

C.

\(2\)units

D.

cannot be determined

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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.

$\dfrac{r}{\sqrt{11}}$

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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

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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?

Image for Geometry & Mensuration, Aptitude:2199-1

A.

$\pi / 4$

B.

$3 \pi / 2$

C.

$\pi / 2$

D.

$\pi$

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