Visualising Solid Shapes Test

Result

Visualising Solid Shapes Test - 22

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Weekly Quiz Competition

Question 1
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What shape are the faces of a cube?

A
Circle

B
Triangle

C
Square

D
Pentagon
Question 2
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How many faces, edges and vertices respectively does the given solid have?

A
$$8, 12, 18$$

B
$$10, 18, 12$$

C
$$8, 18, 12$$

D
$$10, 12, 18$$

Solution

Number of faces $$= 8$$
Number of edges $$= 18$$
Number of vertices $$= 12$$.
Question 3
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Which of the following figures is the solid as viewed from above?

A

B

C

D

Solution

In this figure, base has $$4$$ cubes on either direction and height has $$3$$ cubes.
Only one side is fully covered from front and $$1$$ side has top level row.
If we see from the top, we will get only boundary of cubes.
Hence, option $$D$$ is correct.
Question 4
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Two positions of a dice are shown below. If the face with $$1$$ dot is at the bottom, then the number of dots on the top face is

A
$$2$$

B
$$3$$

C
$$4$$

D
$$5$$

Solution

Given (Ref. image 1)

Find : Dots on the top when $$1$$ dot is at the bottom.

Solution : By seeing both dices we find two faces have same $$3$$ dots.

So Rearrange the dices dots in clockwise.

Here dots $$3$$ are same and different No. of dots are opposite in Both dices respectively as $$5 \leftrightarrow 6 \, ; \, 4 \leftrightarrow 2$$ so Remaining $$3$$ dots are opposite to $$1$$ dot.

Hence the correct answer is option B.
Question 5
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The Euler's formula for polyhedron is

A
$$\displaystyle {V - F + E}=2$$

B
$$\displaystyle {V + F - E}=2$$

C
$$\displaystyle {V - F - E}=2$$

D
$$\displaystyle {V + F - E}=4$$

Solution
Question 6
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The number of corners, edges, and faces of a cuboid respectively are

A

$$8,6,12$$

B
$$4,3,6$$

C
$$4,4,10$$

D
$$8,4,12$$

Solution

A cuboid has $$8$$ corners/vertices, $$12$$ edges and $$6$$ faces.
Hence, option $$A$$ is correct.
Question 7
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How many faces, edges and vertices does the following have and verify using Euler's formula

A
$$pentagonal pyramid$$

B
$$pentagonal prism$$

C
$$square prism$$

D
$$square pyramid$$

Solution

By using Euler's formula :
$$\left( {V - E + F} \right)$$
$$ \Rightarrow 4 - 6 + 4 = 2$$ Polyhexon
$$ \Rightarrow $$ V = Vertices
$$ \Rightarrow $$ E = Edge
and F = Faces
$$ \therefore$$ Pentagonal pyramid has $$(V-E+F=2)$$.
Question 8
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The ratio of the number of sides of a square and the number of edges of a cube is

A
$$1:2$$

B
$$1:3$$

C
$$1:4$$

D
$$2:3$$

Solution

Number of sides of square $$=4$$
Edges of cube $$=12$$
$$\therefore$$ Ratio $$=4:12$$
$$\Rightarrow 1:3$$
Question 9
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Which amongst the following is not a polyhedron ?

A

B

C

D

Solution

A polyhedron has polygons as its faces. Out of the given options, only cone has a curved face.
Therefore, the correct answer is option $$(c).$$
Question 10
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Which of the following is a regular polyhedron ?

A
Cuboid

B
Triangular prism

C
Cube

D
Square prism

Solution

Cuboid, square prism and triangular prism don't have all sides equal.
Only cube has all sides equal, so it has all kind of symmetry and it looks same when seen from all sides.