Visualising Solid Shapes Test

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Visualising Solid Shapes Test - 14

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Question 1
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How can pyramids and cones be alike?

A
Number of sides of its base becomes larger and larger.

B
Number of sides of its base becomes smaller and smaller.

C
Number of sides of its base are equal.

D
None of the above

Solution

The pyramid and cones are alike because their lateral faces meet at a vertex. Also, a pyramid becomes a cone as the number of sides of its base becomes larger and larger.
Question 2
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How are prisms and cylinders alike?

A
Its base becomes larger and larger.

B
Its base becomes smaller and smaller.

C
Either

D
Neither

Solution

In prism and cylinder, base is always constant. Hence, option D is the correct
Question 3
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Madhavi glued $$4$$ white cubes together as shown below. Then she painted the entire figure red. How many faces of the $$4$$ cubes were painted red?

A
$$4$$

B
$$9$$

C
$$18$$

D
$$24$$

Solution

The red coloured faces will be $$4$$ front and $$4$$ back faces, $$2$$ side faces, $$4$$ top faces and $$4$$ botton faces.
$$\Rightarrow 4\times 4+2\times 1=16+2=18$$
Question 4
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A solid object when seen from one side, looks like this (square image).
The same solid, when viewed from the top, looks like this (triangular image).
Identify the figure in three dimensions.

A

B

C

D

Solution

Given: When observed from the top, the figure looks like a triangle

Hence the base of the solid is a triangle.

And when observed from one side, it looks like a square, hence the faces of the solid are squares.

A triangular pyramid has a triangle as its base, and other faces, i.e., lateral faces are parallelograms in shape.

Hence, option "C" is correct.
Question 5
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A solid object when seen from one side looks the same when viewed from the top. Which of these shapes could it be?

A

B

C

D

Solution

It is a cube.
A cube is a three dimensional solid object bounded by six square faces or sides, with three meeting at each vertex.
Since all the faces of the cube are squares, it's top view and front view are same.
Question 6
1 / -0

If $$F = 4$$ and $$V = 3$$, then the value of $$E$$ is: (Use Euler's formula) :

A
$$7$$

B
$$5$$

C
$$4$$

D
$$1$$

Solution

We have Euler formula as:
$$F + V = E + 2$$
$$\because F = 4$$ and $$V = 3$$
$$\Rightarrow 4 + 3 = E + 2$$
$$\Rightarrow E = 5$$
Question 7
1 / -0

The following figure represents a

A
Polygon

B
Convex polyhedron

C
Cylinder

D
None of these

Solution

The following figure represents a Convex polyhedron
Question 8
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Choose the correct statement from the following.

A
A triangle has 3 sides and 4 vertices

B
A solid cylinder has 3 faces

C
All sides of the rectangle are equal

D
A cuboid has 4 flat faces and 12 straight edges

Solution

A. A triangle has $$3$$ sides and $$3$$ vertices.
B. A cylinder has $$3$$ faces - two circular faces at the two ends and the third a curved face.
$$\textbf{Statement B is correct.}$$
C. Only opposite sides of a rectangle are equal.
D. A cuboid has $$6$$ flat faces and $$12$$ edges.
Question 9
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Which of the following solid has six rectangular faces ?

A
Cuboid

B
Pyramid

C
Cone

D
Triangular prism

Solution

Ref fig.
Only Cuboid has six rectangular faces.
Question 10
1 / -0

Which of the given geometric solids has the maximum number of vertices ?

A
Cone

B
Cylinder

C
Cuboid

D
Triangular pyramid

Solution

A cone has $$1$$ vertex.

A cylinder has $$0$$ vertices

A cuboid has $$8$$ vertices.

And a triangular pyramid has $$4$$ vertices

So, a cuboid has the maximum number of vertices among the given shapes.