Visualising Solid Shapes Test

Result

Visualising Solid Shapes Test - 14

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Question 1
1 / -0

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 2
1 / -0

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 3
1 / -0

Which of the following is the top view of the given shape ?

A

B

C

D

Solution

The correct answer is option $$(d).$$
When, seen from top we see $$1$$ square from $$1^{st}$$ row with diamond on it, and $$2$$ blank squares from $$2^{nd}$$ row.
Question 4
1 / -0

The figure shown below can be folded into the shape of a cube. The face marked with the letter L is opposite to the face marked with which letter ?

A
M

B
N

C
Q

D
O

Solution

When we fold the given figure the cube will be as shown in the figure.
It can be observed that $$M$$ comes opposite to $$L$$.
The correct answer is option (a).
Question 5
1 / -0

Which of the following cannot to be true for a polyhedron ?

A
V = 4, F = 4, E = 6

B
V = 6, F = 8, E = 12

C
V = 10, F = 12, E = 20

D
V = 4, F = 6, E = 6

Solution

The correct answer is option $$(d)$$.
Euler's Formula for any polyhedron$$ = F + V -E = 2$$
Where, F = Faces and V = Vertices and $$E =$$ Edges
Option $$A:$$
$$F+V-E=4+4-6=2$$

Option $$B:$$
$$F+V-E=6+8-12=2$$

Option $$C:$$
$$F+V-E=10+12-20=2$$

Option $$D:$$
$$F+V-E=4+6-6=4\neq2$$
Question 6
1 / -0

In a solid if $$ F=V = 5$$, then the number of edges in this shape is

A
6

B
4

C
8

D
2

Solution

The correct answer is option $$(c).$$
For any polyhedron, Euler' s formula ;
$$F + V - E = 2$$
Where, $$F$$ = Face and $$V$$ = Vertices and $$E$$ = Edges
Given, $$ F = V = 5$$
On putting the values of $$F$$ and $$V$$ in the about formulae,
$$ 5 + 5 - E = 2$$
$$\Rightarrow 10 - E = 2$$
$$\Rightarrow E = 8$$
Question 7
1 / -0

Which of the following shapes has a vertex:

A

B

C

D

Solution

The correct answer is option $$(c).$$
Because, a vertex is a sharp corner.
Only cone among the given figures has a sharp corner.
Question 8
1 / -0

Which of the following is valid net for cone?

A

B

C

D
None of these
Question 9
1 / -0

How many faces does a die have

A
$$ 1 $$

B
$$ 2 $$

C
$$ 6 $$

D
$$ 4 $$

Solution

Die have six faces $$1,2,3,4,5, 6 $$
$$n(S)=6$$
Question 10
1 / -0

How many nets are there for cube?

A
$$1$$

B
$$2$$

C
$$3$$

D
$$4$$

Solution