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Plane & Solid Geometry

Total questions: 102

Worksheet time: 51mins

Name
Class
Date
1.

An annulus is a plane figure which is composed of two concentric circles. The area of the annulus can be calculated by getting the difference between the area of the larger cirde and the area of the smaller circle. Also, its area can be calculated by removing the hole. This method is called

a)

Law of extremities

b)

Law of reduction

c)

Law of deduction

d)

Sharp theorem

2.

Each of the faces of a regular hexahedron is a

a)

Square

b)

Triangle

c)

Rectangle

d)

Hexagon

3.

It is a polyhedron of which two faces are equal polygons in parallel planes and the other faces are parallelograms

a)

Tetrahedron

b)

Prism

c)

Frustum

d)

Prismatoid

4.

The apothem of a polygon is ____ of its inscribed circle

a)

Radius

b)

Circumference

c)

Diameter

d)

Length

5.

Each angle of regular dodecagon is equal to

a)

135

b)

150

c)

125

d)

105

6.

The area bounded by two concentric circles is called

a)

Ring

b)

Disk

c)

Annulus

d)

Sector

7.

One-fourth of a great circle is called

a)

Cone

b)

Sector

c)

Quadrant

d)

Arc

8.

Points that lie on the same plane are called

a)

Coplanar

b)

Parallel

c)

Collinear

d)

Oblique

9.

The volume of a circular cylinder is equal to the product of its base and altitude

a)

Axiom

b)

Postulate

c)

Theorem

d)

Corollary

10.

The study of properties of figures in three dimensions

a)

Physics

b)

Plane trigonometry

c)

Solid geometry

d)

Trigonometry

11.

A plane closed curve, all points of which are the same distance from a point within, called center.

a)

Polyhedron

b)

Polygon

c)

Circle

d)

Ellipse

12.

What is the angle of π and less than 2π?

a)

Straight line

b)

Obtuse angle

c)

Oblique angle

d)

Acute angle

13.

What is the value in degrees of 1 radian?

a)

90°

b)

57.3°

c)

60°

d)

33°

14.

Prisms are named according to their ____

a)

Diagonals

b)

Sides

c)

Vertices

d)

Bases

15.

In plane geometry, two circular arcs that together make up a full circle are called

a)

Coterminal arcs

b)

Conjugate arcs

c)

Congruent arcs

d)

Half arcs

16.

Polygons are classified according to the number of ____

a)

Vertices

b)

Sides

c)

Diagonals

d)

Angles

17.

When two planes intersects with each other, the amount of divergence between the two planes in expressed by measuring the

a)

Dihedral angle

b)

Plane angle

c)

Polyhedral angle

d)

Reflex angle

18.

An angular unit equivalent to 1/4000 of the circumference of a circle is called

a)

Mil

b)

Degree

c)

Radian

d)

Grad

19.

Express 45° in mils

a)

80

b)

800

c)

1600

d)

2700

20.

The arc length equal to the radius of the circle is called

a)

Radian

b)

Quarter sector

c)

Sector

d)

Semicircle

21.

A five-pointed star is also known as

a)

Pentagon

b)

Pentatron

c)

Pentagram

d)

Quintagram

22.

If two or more lines have a single point which lies on all of them, then they are

a)

Collinear

b)

Coplanar

c)

Concurrent

d)

Conjugate

23.

The action of bringing one geometric figure into coincidence with another is called

a)

Transposition

b)

Translation

c)

Superposition

d)

Projection

24.

A line that intersect two or more lines at distinct points

a)

Tangent line

b)

Transversal

c)

Bisector

d)

Median

25.

An arc length equal to the radius of a circle

a)

Grad

b)

Radian

c)

Degree

d)

Mil

26.

An angle which is 1/400th of the full revolution

a)

Gon

b)

Mil

c)

Degree

d)

Radian

27.

Another term for gon

a)

Grad

b)

Mil

c)

Centesimal degree

d)

A and C

28.

An angle whose vertex is a point on the circle and whose sides are chords in known as

a)

Interior angle

b)

Vertical angle

c)

Actue angle

d)

Inscribed angle

29.

An angle greater than the right angle but less than a straight angle

a)

Acute angle

b)

Obtuse angle

c)

Reflex angle

d)

Oblique angle

30.

Any angle greater than a straight angle but less than two straight angles is known as ____ angle

a)

Compliment

b)

Supplement

c)

Complex

d)

Reflex

31.

The angle formed by the prolongation of one side and the adjacent side of the polygon.

a)

Interior angle

b)

Acute angle

c)

Exterior angle

d)

Explementary angle

32.

Two angles which have the same vertex and the sides of one are form by extending the sides of the other

a)

Adjacent angles

b)

Vertical angles

c)

Deflection angles

33.

Another term for exterior angle

a)

Vertical angle

b)

Inscribed angle

c)

Reflex angle

d)

Deflection angle

34.

What is the sum of all deflection angles in given polygon?

a)

Always less than 360°

b)

Always equal to 360°

c)

Always greater than 360°

d)

Always equal to 180°

35.

The coterminal angle of 120° is

a)

240°

b)

-240°

c)

480°

d)

-480°

36.

Two planes intersect each other. What is the term for the angle formed perpendicular to the intersection of two planes?

a)

Solid angle

b)

Plane angle

c)

Base angle

d)

Dihedral angle

37.

When a terminal side of an angle coincides with an axis, the angle is a

a)

Coterminal angle

b)

Right angle

c)

Quandrantal angle

d)

Reflex angle

38.

If the exterior angle of a polygon is obtuse, its corresponding interior angle is

a)

An acute angle

b)

Also an obtuse angle

c)

A reflex angle

d)

Always greater than 160°

39.

The measure of 2.25 revolutions counterclockwise is

a)

835°

b)

805°

c)

810°

d)

815°

40.

Solid angles are measured in

a)

Mil

b)

Radians

c)

Steradians

d)

Circular mils

41.

What is the largest measure (in steradians) of the solid angle?

a)

b)

c)

d)

π

42.

Steradians measure in space in analog of ____ measured in the plane

a)

Radians

b)

Degrees

c)

Mils

d)

Grads

43.

A part of a circle called

a)

Sector

b)

Segment

c)

Chord

d)

Arc

44.

It is a union of the chord of a circle and the intercepted arc

a)

Sector

b)

Segment

c)

Lune

d)

Zone

45.

A _____ of a circle in the figure bounded by two radii and the intercepted arc

a)

Major arc

b)

Minor arc

c)

Segment

d)

Sector

46.

As the area of the circle increases, the ratio of its circumference to its diameter

a)

Increases

b)

Remains constant

c)

Decreases

d)

Will be equal to 1

47.

A circle is said to be _____ to a polygon having the same perimeter with that of the circle

a)

Congruent

b)

Isoperimetric

c)

Proportional

d)

Convex

48.

Which of the following is NOT a property of a circle?

a)

Through 3 points not in a straight line, only one circle can be drawn

b)

A tangent to a circle is perpendicular to the radius at the point of tangency and conversely

c)

An inscribed angle is measured by one half of the intercepted arc.

d)

The arcs of two circles subtended by equal central angles are always equal

49.

All circles having the same center but of unequal radii are called

a)

Concentric circles

b)

Eccentric circles

c)

Inner circles

d)

Pythagorean circles

50.

Two chords of a circle which joins a point on the circle to the end points of a diameter and forms a right angle

a)

Complementary chords

b)

Supplementary chords

c)

Focal chords

d)

Chords of contrast

51.

The center of the inscribed circle of a triangle is known as ____ of the triangle

a)

Circumcenter

b)

Incenter

c)

Excenter

d)

Orthocenter

52.

Supplementary chords are two chords which join a point on the circle to the endpoirts of a diameter. The supplemental chords subtend a/an ____ angle.

a)

Acute

b)

Right

c)

Obtuse

d)

Reflex

53.

A circle or radius R has a curvature of

a)

R2

b)

1/R

c)

2R

d)

√R

54.

A polygon is ____ when no side, when extended, will pass through the interior of the polygon

a)

Convex

b)

Equilateral

c)

Isoperimetric

d)

Similar

55.

A polygon is said to be regular polygon if its is

a)

Convex

b)

All sides are congruent

c)

All angles are congruent

d)

All of the above

56.

Polygon inscribed in the same circle called

a)

Concentric polygons

b)

Ocentric polygons

c)

Concylic polygons

d)

Orthocentric polygons

57.

If n is the number of sides of a polygon, then the sum of all interior angles of a polygon is expressed as

a)

(n+2) 180°

b)

(n/2) 180°

c)

(n-2) 180°

d)

(n/2)(n-3)

58.

If n is the number of sides of a polygon, then the number of diagonals of a polygon is expressed as

a)

n!

b)

(n-1)!

c)

(n/2)(n-3)

d)

(n/3)(n-2)

59.

What do you call a polygon with 11 sides?

a)

Unagon

b)

Unogon

c)

Undecagon

d)

Dodecagon

60.

Pentagon is to 5 sides as ____ is to 11 sides

a)

Heptagon

b)

Septagon

c)

Unidecagon

d)

Hendecagon

61.

A polygon having 12 sides is called

a)

Bidecagon

b)

Dodecagon

c)

Nonagon

d)

Pentedecagon

62.

A polygon of 100 sides is called

a)

Chilliagon

b)

Ennagon

c)

Perigon

d)

Milliagon

63.

The highest point of a figure relative to a baseline or plane is called

a)

Summit

b)

Highest ordinate

c)

Terminal point

64.

Indicate the false statement

a)

A trapezoid is a quadrilateral two and only two of whose sides are parallel.

b)

The sum of two sides of a triangle is greater than the third side and their difference is less than the third side.

c)

A diagonal of a polygon is a iine joining any-non-consecutive vertices.

d)

Two angles are complementary if their sum is equal to 180°

65.

Which of the following statements is correct?

a)

All right-angled triangles are similar

b)

All isosceles triangles are similar

c)

All equilateral triangles are similar

d)

All rectangles are similar

66.

A quadrilateral with no sides parallel.

a)

Trapezoid

b)

Rhombus

c)

Rhomboid

d)

Trapezium

67.

Which of the following BEST describes Ptolemy's theorem?

a)

It is use only for quadrilaterals

b)

It is just a modification of Brahmagupta's theorem

c)

It is used only for cyclic quadrilaterals

d)

The sum of the square of the sides is equals to the square of the diagonals of a guven quadrilateral

68.

The five-pointed star described by the diagonals of a regular Pentagon

a)

Perigon

b)

Pentegram

c)

Penacle

d)

Pentegram or penacle

69.

The geometric figure remaining after a parallelogram has been removed from one corner of a larger similar polygon.

a)

Google

b)

Gnomon

c)

Gaussian plane

d)

Lozenge

70.

An oblique-angled parallelogram with four sides equal is called

a)

Rhombus

b)

Diamond

c)

Lozenge

d)

All of the above

71.

A non-convex quadrilateral with two pairs of adjacent equal sides is called

a)

Trapezium

b)

Kite

c)

Deltroid

d)

Diamond

72.

What is another term for a parallelogram?

a)

Rectangle

b)

Quadrangle

c)

Diamond

d)

Rhomboid

73.

A solid cut of a given solid by two non parallel planes is called

a)

Frustum

b)

Prism

c)

Truncated prism

d)

Prismatoid

74.

A polyhedron having bases two polygons in parallel planes and for lateral faces triangles or trapezoids with one side lying on the other base of the polyhedron

a)

Pyramid

b)

Cone

c)

Prismatoid

d)

Truncated prism

75.

Portion of regular solid left after cutting off the upper part by a plane parallel to the base

a)

Frustum

b)

Ungula

c)

Truncated solid

d)

Prismatoid

76.

Body of space bounded by surface every point of which is equidistant from a point within

a)

Circle

b)

Sphere

c)

Spheroid

d)

Ellipsoid

77.

A solid bounded by a zone and the planes of the zone's base

a)

Spherical sector

b)

Spherical segment

c)

Lune

d)

Spherical excess

78.

The intersection of the sphere and the plane through the center is called

a)

Great circle

b)

Small circle

c)

Poles

d)

Polar distance

79.

The portion of a sphere enclosed between two great semi circles having common end points including the semi circle

a)

Spherical excess

b)

Spherical segment

c)

Zone

d)

Lune

80.

A portion of the surface of a sphere including between two parallel planes

a)

Spherical excess

b)

Spherical segment

c)

Zone

d)

Lune

81.

If R is the radius of the sphere and h s the distance between two parallel plane the area of the zone is

a)

2πRh

b)

4πRh

c)

πh²(3R - h)/3

d)

4π(R - h)

82.

The solid bounded by two great circles and the surface of a sphere is known as

a)

Spherical zone

b)

Spherical segment

c)

Spherical cone

d)

Spherical wedge

83.

A cone or cylinder with its top cut off by plane oblique to the base

a)

Frustum

b)

Prismoid

c)

Prismatoid

d)

Ungula

84.

A term given to cylinder with elliptical cross section

a)

Cylindroid

b)

Cylindoid

c)

Ovaloid

d)

Deltroid

85.

A doughnut-like surface of revolution generated by rotating the circle through 360° in space about a line in its plane but now passing through the circle

a)

Torus

b)

Annulus

c)

Anchor

d)

All of the above

86.

A regular solid star in a shape that is radiating from center like rays of star

a)

Pentagram

b)

Pentagon

c)

Stellated solid

d)

Archimedean solid

87.

Formed by intersection of rays from one point reflected of refracted from a curvature surface

a)

Envelop

b)

Caustic

c)

Evolute

d)

Pencil

88.

There regular polyhedron is a solid with all its faces identical regular polygons. The regular polyhedrons are knows as

a)

Euclidean solids

b)

Pythagorean solids

c)

Platonic solids

d)

Newtonian solids

89.

There are how many regular polyhedra known to man

a)

5

b)

3

c)

7

d)

10

90.

An icosahedron is a regular polyhedron of _____ faces

a)

12

b)

14

c)

16

d)

20

91.

A regular polyhedron with 6 sides is called

a)

Dodecahedron

b)

Hexahedron

c)

Tetrahedron

d)

Octahedron

92.

The face of a regular tetrahedron is a

a)

Square

b)

Pentagon

c)

Hexagon

d)

Triangle

93.

The face of a regular octahedron is a

a)

Square

b)

Pentagon

c)

Hexagon

d)

Triangle

94.

The face of a regular dodecahedron is a

a)

Square

b)

Pentagon

c)

Hexagon

d)

Triangle

95.

The face of a regular icosahedron is a

a)

Square

b)

Pentagon

c)

Hexagon

d)

Triangle

96.

Which regular polyhedron does not have a face a triangle

a)

Tetrahedron

b)

Octahedron

c)

Icosahedron

d)

Dodecahedron

97.

How many edges are there in a dodecagon

a)

6

b)

12

c)

30

d)

8

98.

A tetrahedron has ____ vertices

a)

4

b)

3

c)

6

d)

5

99.

Given two solids and a plane. Supposed that every plane parallel to the given plane intersecting one of the two solids, also intersects the other and given cross-sections with the same area then the two solids have the same volume. This is known as the

a)

Unit postulate

b)

Plane postulate

c)

Parallel postulate

d)

Cavallieri`s postulate

100.

Who formulated the cavalieri`s principle

a)

Harold cavalieri

b)

Buenaventura cavalieri

c)

Joefry cavalieri

d)

Carl cabalieri

101.

A line segment that is divided into two segments a greater a and a smaller b such that the length of a + b is to a and a is to b. Such division is known as

a)

Golden segment

b)

Golden ratio

c)

Golden proportion

d)

All of the above

102.

The volume of a paraboid is equal to ____ the volume o circumscribing cylinder

a)

1/3

b)

1/2

c)

1/4

d)

2/3