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Understanding Elementary Shapes Test - 8

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Understanding Elementary Shapes Test - 8
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  • Question 1
    1 / -0
    How many degrees does the minute hand of a clock subtend in 10 minutes?
    Solution
    We know that the minute hand completes one complete revolution in 60 minutes or 1 hour.

    Minute hand subtends an angle of 360o in 60 minutes.
    Angle subtended by a minute hand in 60 minutes = 360o
    Angle subtended by a minute hand in 1 minute = = 6o
    Angle subtended by a minute hand in 10 minutes = 6 × 10 = 60o

    Option (2) is correct.
  • Question 2
    1 / -0
    What cross section will be obtained when an upright circular cylinder is sliced horizontally?
    Solution


    In the above diagram, an upright cylinder is cut horizontally along the line AB and the cross section obtained is shaded.
    It is clear from the diagram that the cross section obtained is a circle.
    Hence, option 2 is correct.
  • Question 3
    1 / -0
    Which of the following statements is incorrect?
    Solution
    (i) All angles of rectangles are 90°.
    This statement is correct because a rectangle has four right angles.

    (ii) Trapezium has two pairs of opposite parallel sides.
    This statement is incorrect because trapezium has only one pair of opposite parallel sides.

    (iii) Opposite angles in rhombus are equal.
    This statement is correct because a rhombus is a flat shape with 4 equal straight sides. Opposite sides are parallel and opposite angles are equal.

    (iv) Square has all 4 equal sides.
    This statement is correct as we know that square is a geometric shape that belongs to the quadrilateral family because it has 4 sides. The 4 sides are of same length and are parallel to each other.

    Option (2) is correct.
  • Question 4
    1 / -0
    Directions: Find A, B, C and D.

    A triangular prism has ___(A)___ base, ___(B)___faces, ___(C)___ corners and ___(D)___ edges.
    Solution

    In the above figure the faces are shown by letters and the vertices are shown by numbers.
    A triangular prism is a three-sided prism. It is a polyhedron made of a triangular base, 5 faces, 6 corners and 9 edges.

    Option (1) is correct.
  • Question 5
    1 / -0
    How many right angles does the hour hand of a clock turn when it moves from 12 to 9?
    Solution


    It starts from 12 and covers digits 1 to 9. So, hour hand turns by three right angles.
    So, from 12 to 9, there are 3 right angles.
    Option (3) is correct.
  • Question 6
    1 / -0
    Rustom is the captain of a ship. The ship is initially facing north. Then, the ship makes half a turn in clockwise direction. Which direction is the ship facing after making the turn?
    Solution
    The rotation of the ship is illustrated with the help of the diagram below:

    The arrows indicate the direction of rotation of the ship.
    After making half a turn in clockwise direction, the ship faces south.
  • Question 7
    1 / -0
    'XY is parallel to ST' is symbolically written as
    Solution
    So, 'XY is parallel to ST' is written as .

    Option (2) is correct.
  • Question 8
    1 / -0
    A perpendicular bisector of a line segment is a line segment perpendicular and passing through _______ of the figure.
    Solution
    A perpendicular bisector of a line segment is a line segment perpendicular to and passing through the midpoint of a figure.
    For example:

    In the above figure, if lm is a perpendicular bisector of line segment AB, then point P will be the mid-point of line segment AB or AP = PB.
    Option (3) is correct.
  • Question 9
    1 / -0
    Which of the following statements is correct?
    Solution
    (I) All sides of a parallelogram are of different length.
    This statement is incorrect because a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

    (II) All sides of a rhombus are equal. This statement is correct. A rhombus is a flat shape with 4 equal straight sides and its diagonals are perpendicular to each other.

    (III) Rectangle is not a parallelogram.
    This statement is incorrect because a rectangle is considered a special case of a parallelogram because a parallelogram is a quadrilateral with 2 pairs of opposite, equal and parallel sides. A rectangle is a quadrilateral with 2 pairs of opposite, equal and parallel sides, but also forms right angles between adjacent sides.

    (IV) A parallelogram has no obtuse angle.
    This statement is incorrect because as adjacent angles of a parallelogram are supplementary and opposite angles are equal, if one angle is obtuse, adjacent angle would be acute and opposite angle would be obtuse. Hence, a parallelogram can have no more than two obtuse angles.

    Option (2) is correct.
  • Question 10
    1 / -0
    How many diagonals does a pentagon have?
    Solution
    A regular pentagon has 5 diagonals.
    The diagonals are: AD, AC, BE, BD, CE

  • Question 11
    1 / -0
    Which of the following is a parallelogram?
    Solution
    A rhombus is a flat shape with 4 equal straight sides. All sides of rhombus have equal length. Opposite sides of a rhombus are parallel and opposite angles are equal. So, it is a parallelogram.

    Option (2) is correct.
  • Question 12
    1 / -0
    A tetrahedron has ____ edges.
    Solution


    In geometry, a tetrahedron, also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges and four vertices.
    So, we can say that a tetrahedron has 6 edges.

    Option (2) is correct.
  • Question 13
    1 / -0
    I am a 3-D figure. I have 8 faces, 6 vertices and 12 edges. Who am I?
    Solution


    An octahedron is a polyhedron with eight faces, twelve edges and six vertices.

    Option (1) is correct.
  • Question 14
    1 / -0
    What does a cuboid have?
    Solution
    A cuboid is a 3-D figure which has 6 faces and 12 edges.

  • Question 15
    1 / -0
    Which of the following solids will not have the same number of faces and vertices?
    Solution
  • Question 16
    1 / -0
    A truck moves a certain distance and comes to rest. To cover that distance, the wheels of the truck make three-and-a-half revolutions. The number of straight angles through which each wheel turns is
    Solution
    1 revolution of a wheel = 2 straight angles
    3.5 revolutions of a wheel = 3.5 x 2 = 7 straight angles
    So, option (3) is correct.
  • Question 17
    1 / -0
    A quadrilateral-shaped table has only two sides equal. Which of the following is not a possible shape for the table?
    Solution
    Rectangle is a quadrilateral with four right angles. The opposite sides of rectangle are equal.
    Square is also a quadrilateral with four right angles. But all the 4 sides of a square are equal and are parallel to each other. Hence, it cannot the shape of table given in question.
    Parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.
    Hence, option (3) is correct.
  • Question 18
    1 / -0
    Which of the following nets is used to make a cylinder?
    Solution

    In figure 1, some letters are assigned to the different parts of cylinders.
    When a cylinder is converted into 2 dimension diagram the net of the cylinder will be as figure 2.
    Hence, option 4 is correct.
  • Question 19
    1 / -0
    Which of the following statements is false?
    Solution
    (I) The interior angles of quadrilaterals add to 360°.
    This is correct.
    (II) Any quadrilateral with 4 right angles is not a trapezium. A quadrilateral with 4 right angles can be either Square or Rectangle.
    (III) A diamond shape is a good example of a rhombus.
    A rhombus is a flat shape with 4 equal straight sides. A rhombus looks like a diamond. All sides have equal length.
    (IV) A kite quadrilateral features 2 pairs of adjacent sides that are of equal length.
    This statement is correct.
    Option (2) is correct.
  • Question 20
    1 / -0
    What shape is the face of a cuboid?
    Solution
    Faces of cuboid are rectangle because a cuboid is a 3D shape. Cuboids have six faces, which form a convex polyhedron. Broadly, the faces of the cuboid can be any quadrilateral. More narrowly, cuboids are made from 6 rectangles, which are placed at right angles. A cuboid that uses all square faces is a cube.
    The shape of a face of cuboid can be understood by the following diagram.

  • Question 21
    1 / -0
    How many right angles do we cover if we turn from north to south?
    Solution
    If we turn from north to south, we turn by 2 right angles as shown below.

  • Question 22
    1 / -0
    Two faces of a cube meet at a line segment. What is this line segment called?
    Solution
    Two faces of a cube meet at an edge.

  • Question 23
    1 / -0
    A square pyramid consists of
    Solution
    A squarer pyramid has triangular faces and a square base.

  • Question 24
    1 / -0
    Number of vertices of a square based pyramid are ______ number of vertices of a regular cube.
    Solution



    Vertices of a square based pyramid = 5
    Vertices of regular cube = 8
    Option (1) is correct.
  • Question 25
    1 / -0
    A man is standing facing south. Which direction will he face if he makes (a) revolution anti-clockwise and (b) revolution clockwise ?
    Solution
    A revolution make him face west from south.

    1 complete revolution will bring him back to south. After that, he will take (3/4) of a revolution.

    Then, will turn him to North from South.


  • Question 26
    1 / -0
    Directions: State T for true and F for false.

    (a) (b) (c) (d)
    (A) F F T T
    (B) F T F T
    (C) T T F F
    (D) T F T F

    (a) A quadrilateral is a four sided polygon.
    (b) All the four sides of a square are equal.
    (c) One pair of diagonally opposite angles of a kite are equal.
    (d) Half a revolution is a right angle.
    Solution
    A quadrilateral has a four sides and is a closed shape. So, (a) is true.
    A square has all its sides and angels equal. So, (b) is true.
    A kite has one pair of diagonal angles equal, which is not true. So, (c) is false.
    Half a revolution is 180 degrees which is a straight angle. So, it is false. (d) is false.
    Option (3) is correct.
  • Question 27
    1 / -0
    Select the INCORRECT match from the following.


    Solution

  • Question 28
    1 / -0
    Which of the following figures satisfy the given condition?

    Figure (i) faces: 6, edges: 12 and vertices: 8
    Figure (ii) faces: 5, edges: 8 and vertices: 5
    Solution

    Fig (i) cube has 6 faces, 12 edges and 8 vertices and Fig (ii) square pyramid has 5 faces, 8 edges and 5 vertices.
    Option (4) is correct.
  • Question 29
    1 / -0
    Directions: Fill in the blanks.

    (A) Equal Square Trapezium Kite
    (B) Equal Trapezium Square Kite
    (C) Equal Kite Trapezium Square
    (D) Equal Square Kite Trapezium

    (i) The opposite sides of a rectangle are _A__.
    (ii) A quadrilateral having all the sides equal is called __B__.
    (iii) A parallelogram having equal one pair of diagonally opposite angles is called __C___.
    (iv) A quadrilateral having exactly one pair of parallel sides is called __D___.
    Solution
    (i) Opposite sides of a rectangle are equal.
    (ii) Square has all the sides equal.
    (iii) Kite has one pair of diagonally opposite angles.
    (iv) Trapezium has only one pair of parallel sides.
    Option (4) is correct.
  • Question 30
    1 / -0
    Which of the following statements is correct?
    Solution
    The complete angle or the angle in one complete revolution = 360o
    th of 360o or a revolution = .
    Therefore, a right angle is of a revolution.
    Option (1) is correct.
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