Cuboid

Q.

Assertion: If the inner dimensions of a cuboidal box are $50cm\times 40cm\times 30cm,$ then the length of the longest rod that can be placed in the box is $50\sqrt{2}cm$.
Reason: The line joining opposite corners of a cuboid is called its diagonal.
Also, length of longest rod $=$ length of diagonal $=\sqrt{l^2+b^2+h^2}$

1. Assertion is correct but Reason is incorrect

2. Both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion

3. Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.

4. Assertion is incorrect but Reason is correct.

Q. There is a thin metal plate having length, breadth, and thickness as 2M mm, 2K mm and 1 mm, respectively. If ‘N’ plates are placed one on top of the other, then what is the object formed. Also, find its volume in $m{m}^3$?
(2 Marks)

Q.

Match the following.

$\begin{array}{cc}\left(a\right)edge& \left(i\right)point\\ \left(b\right)vertex& \left(ii\right)1-dimension\\ \left(c\right)face& \left(iii\right)2-dimension\end{array}$

1. (a) - (iii), (b) - (i), c-(ii)

2. (a) - (i), (b) - (iii), c-(ii)

3. (a) - (ii), (b) - (i), c-(iii)

4. (a) - (i), (b) - (ii), c-(iii)

Q. If the inner dimensions of a cuboidal box are 50 cm $\times$ 40 cm $\times$ 30 cm, then the length of the longest rod that can be placed in the box is

1. $50\text{cm}$
2. $120\text{cm}$
3. $50\sqrt{2}\text{cm}$
4. $50\sqrt{3}\text{cm}$

Q.

Cuboids can be formed by stacking

[Stacking means placing objects on top of one another]

1. Rectangles

2. Squares

3. Triangles

4. Parallelograms

Q. A right circular cone is generated by revolving a right-angled triangle about one of the sides containing the _____.

1. vertical angle
2. obtuse angle
3. straight angle
4. right angle

Q.

A paper is rectangular in shape with negligible thickness. A stack of papers is arranged one above the other.

S1 : The resulting figure is three dimensional.

S2 : The figure is called a cuboid.

1. S1 is true but S2 is false

2. S1 is false but S2 is true

3. S1 and S2 are true

4. S1 and S2 are false

Q.

The length of the longest bar that can be fixed in a room of dimensions 12 m $\times$ 9 m $\times$ 8 m is ___ m.

Q.

A small indoor greenhouse is made entirely of glass panes held together with tape. It is $30cm$ long, $25cm$ wide and $25cm$ high. How much of tape is needed for all the 12 edges?

1. $230cm$

2. $320cm$

3. $302cm$

4. $203cm$

Q.

The surface area of a box which is in the form of a cuboid whose dimensions are
l x b x h is:

1. 2(lb + bh + hl)

2. lb + bh + hl

3. 2(lh + bh)

4. lh + bh