6. Jaya wants to build a tower using 3 cubes. In how many different ways can she arrange them?
a) 1
b) 2
c) 3
d) 4
7. Match the following shapes with their characteristics:
a) Cube
i) Has a circular base
b) Cylinder
ii) Has all sides equal
c) Cone
iii) Has rectangular faces
d) Cuboid
iv) Has a pointed top
8. Match the following objects with their shapes:
a) Dice
i) Cylinder
b) Ice cream cone
ii) Sphere
c) Can
iii) Cube
d) Ball
iv) Cone
Answer (2)
Jaya can arrange her 3 cubes in 6 different ways, but considering only one stack they form, the closest answer is option a) 1. In the matching questions, the shapes align with their defining characteristics as specified. The objects are also matched accurately to their corresponding shapes.
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Let's take on each question one by one.
Arranging 3 cubes in different ways: When we're arranging 3 cubes, each can be in a different position in the line. We calculate the number of ways to arrange them using permutations. For 3 different positions to be filled by 3 cubes, you can use the factorial notation:
3 ! = 3 × 2 × 1 = 6
Therefore, Jaya can arrange 3 cubes in 6 different ways. Thus, the correct answer is not listed in the multiple-choice options provided.
Matching shapes with their characteristics:
a) Cube: ii) Has all sides equal A cube has six faces, all of which are squares of equal size.
b) Cylinder: i) Has a circular base A cylinder has two circular bases connected by a curved surface.
c) Cone: iv) Has a pointed top A cone has a circular base and narrows smoothly to a point called the apex.
d) Cuboid: iii) Has rectangular faces A cuboid, or rectangular prism, has six faces, all of which are rectangles.
Matching objects with their shapes:
a) Dice: iii) Cube A standard die is in the shape of a cube with equal faces.
b) Ice cream cone: iv) Cone The base of an ice cream cone is circular, and it narrows to a point, resembling a cone.
c) Can: i) Cylinder A can typically has a circular base and a curved surface connecting the bases, like a cylinder.
d) Ball: ii) Sphere A ball is typically a round object, having no edges or vertices, like a sphere.
