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If the length of each side of a regular tetrahedron is $12 cm$ , then the volume of the tetrahedron is:

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Important Questions on Geometry

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Quantitative Abilities>Geometry>Geometry>2D Geometrical Shapes

In the given diagram, point R and Q are on PS. ÐPQT = x°, ÐRQT = (x – 50)° and ÐTUR = (x + 25°). find the value of ÐURS.

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MEDIUM

Quantitative Abilities>Geometry>Geometry>2D Geometrical Shapes

$5 : 18$ is the ratio of the length and perimeter of a rectangle. What would be the ratio of its length and breadth?

EASY

Quantitative Abilities>Geometry>Geometry>2D Geometrical Shapes

Read the given question and decide which of the following information is sufficient to answer the question.

What is the value of 0?

Information :

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(II) 0 < q < 90°

EASY

Quantitative Abilities>Geometry>Geometry>2D Geometrical Shapes

How many tangents can be drawn to two circles, whose radii are equal to

4 c m

and

5 c m

respectively and the distance between the two centres is

5 c m

EASY

Quantitative Abilities>Geometry>Geometry>2D Geometrical Shapes

A hall is

15 m

long and

12 m

broad. The sum of the areas of the floor and the ceiling is?(in square meters).

EASY

Quantitative Abilities>Geometry>Geometry>2D Geometrical Shapes

The distance between the centres of two circles having radii

5 c m

and

6 c m

\sqrt{10} c m

. Find the length (in

c m

) of direct common tangent.

MEDIUM

Quantitative Abilities>Geometry>Geometry>2D Geometrical Shapes

∆ A B D

C

is the midpoint of

B D

. If

A B

= 10

cm, AD

= 12

cm and

A C

= 9

cm, then

B D = ?

EASY

Quantitative Abilities>Geometry>Geometry>2D Geometrical Shapes

The area of an equilateral triangle is

18 \sqrt{3}

sq. units. Find the value of the side (in units) of the triangle.

EASY

Quantitative Abilities>Geometry>Geometry>2D Geometrical Shapes

If the interior angle of a regularpolygon is $108 °$ , then it is a-

1. Octagon

2. Hexagon

3. Pentagon

4. Tetragon

MEDIUM

Quantitative Abilities>Geometry>Geometry>2D Geometrical Shapes

If the length of a rectangle is decreased by

5

metres and breadth increased by

3

metres, its area decreases by

9 m^{2}

. If its length is increased by

3 m

and breadth by

2 m

, its area increases by

67

m^{2}

. What is the length of the rectangle ?

EASY

Quantitative Abilities>Geometry>Geometry>2D Geometrical Shapes

The length of one side and the diagonal of a rectangle are

10 cm

and

26 cm

respectively. Find the length of the other side (in

cm

HARD

Quantitative Abilities>Geometry>Geometry>2D Geometrical Shapes

If the distance between the foci of an ellipse is half the length of its latus rectum, then the eccentricity of the ellipse is:

EASY

Quantitative Abilities>Geometry>Geometry>2D Geometrical Shapes

Find the perimeter (in

c m

) of a semicircle of radius

7 c m

EASY

Quantitative Abilities>Geometry>Geometry>2D Geometrical Shapes

If the distance between the foci of an ellipse is

6

and the distance between its directrix is

12,

then the length of its latus rectum is

EASY

Quantitative Abilities>Geometry>Geometry>2D Geometrical Shapes

An arc length of

16 π

units subtends an angle of

240

degrees. Find the radius (in unit) of the circle.

HARD

Quantitative Abilities>Geometry>Geometry>2D Geometrical Shapes

The two circles with radii $6 c m$ and $3 c m$ centred at the point $P$ and $Q$ respectively. A transverse common tangent $A C$ to the both circles cuts line Joining $P$ and $Q$ at the point $B$ such that $A B = 8 c m$ . Calculate the length (in cm.) of $P Q$ .

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EASY

Quantitative Abilities>Geometry>Geometry>2D Geometrical Shapes

△ A B C,

the measure of angle

∠ A B C

90 °

. If

tan A = \frac{12}{5},

and

A B = 1 c m

, then what is the length (in

c m

) of side

B C ?

MEDIUM

Quantitative Abilities>Geometry>Geometry>2D Geometrical Shapes

The exterior angle of a regular polygon is

72 °

. What would be the sum of all its interior angles?

MEDIUM

Quantitative Abilities>Geometry>Geometry>2D Geometrical Shapes

If a point

P (x, y)

moves along the ellipse

\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1

and if

C

is the centre of the ellipse, then the sum of maximum and minimum values of

C P

MEDIUM

Quantitative Abilities>Geometry>Geometry>2D Geometrical Shapes

The equation of the circle passing through the foci of the ellipse

\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1

, and having centre at

(0, 3)

If the length of each side of a regular tetrahedron is 12 cm, then the volume of the tetrahedron is:

Important Questions on Geometry

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If the length of each side of a regular tetrahedron is $12 cm$ , then the volume of the tetrahedron is: