Cuboid

Q. Find the length of the longest pole that can be placed in a room 12m long, 8m broad and 9m high.

Q.

The length of the longest rod that can be placed in a room of dimensions $(10m\times 10m\times 5m)$

(a) 15 m (b) 16 m (c) $\sqrt{5}m$ (d) 12 m

Q.

$\text{What is the maximum length of a pencil that can be placed in a rectangular box of dimensions}(8cm\times 6cm\times 5cm)?(Given\sqrt{5}=\mathrm{2.24.})\left(a\right)8cm\left(b\right)9.5cm\left(c\right)19cm\left(d\right)11.2cm$

Q.

Find the total surface area of a solid hemisphere of radius $r$

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

1. acute angle
2. obtuse angle
3. right angle

Q. The dimensions of a hall is 10 m × 9 m × 8 m. Find the cost of whitewashing the walls and ceiling at the rate of ₹8.50 per m².

1. 3349

Q. An oil tin in the shape of a cuboid has dimensions 26 cm x 26 cm x 45cm. The total cost for making 20 such tins at
₹10/$m^2$ is .

1. ₹ 120.64
2. ₹ 125.60
3. ₹ 128.60

Q. The length of the longest diagonal of a cuboid of dimensions 3 cm × 4 cm × 12 cm is

1. 12 cm
2. 13 cm
3. 8 cm
4. $4\sqrt{10}cm$

Q. The sum of total surface area of a hemisphere of radius $r$ and the total surface area of a sphere of radius $\frac{r}{2}$ is

1. $5\pi r^2$
2. $4\pi r^2$
3. $3\pi r^2$
4. $6\pi r^2$

Q.

A cuboid has total surface area of $372c{m}^2$ and its lateral surface area is $180c{m}^2,$ find the area of its base.

Q. A room is 15 metres long, 4 metres broad and 3 metres high. Find the cost of whitewashing its four walls at ₹0.5 per $m^2$.

1. ₹60
2. ₹57
3. ₹55
4. ₹52

Q.

A hollow prism with a square base of side 16 cm contains water 10 cm high. If a solid cube of side 8 cm is immersed in it, what will be the new height of water level in the prism?

1. 2 cm

2. 12cm

3. 10 cm

4. 14 cm

Q.

Find the total surface area of a hemisphere of radius $10\mathrm{cm}$. [Use $\mathrm{\pi }=3.14$]

Q. The height and base radius of a cone are $6cm$ and $8cm$ respectively. The curved surface area of the cone is:

1. $14\pi {cm}^2$
2. $60\pi {cm}^2$
3. $80\pi {cm}^2$
4. $48\pi {cm}^2$

Q.

A wooden bookshelf has external dimensions as follows: Height = 110 cm, Depth = 25 cm, Breadth = 85 cm (see the given figure). The thickness of the plank is 5 cm everywhere. The external faces are to be polished and the inner faces are to be painted. If the rate of polishing is 20 paise per cm² and the rate of painting is 10 paise per cm², find the total expenses required for polishing and painting the surface of the bookshelf.

Q. If the length of a cuboid is thrice its breadth and the breadth is twice its height, then the ratio of TSA to LSA of cuboid will be ___.

1. 5: 2
2. 5: 3
3. 8: 2
4. 5: 4

Q.

Which of the following is not a simple closed figure?

1. 

2. 

3. 

4. 

Q.

A Minimal Spanning Tree of a graph $\mathrm{G}$ Is

1. A Tree

2. Minimum Weights

3. A Spanning Subgraph

4. All Of These

Q.

Question 2
Theinner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm.The length of the pipe is 35 cm. Find the mass of the pipe, if $1c{m}^3$ of wood has a mass of 0.6 g.
$[Assume\pi =\frac{22}{7}]$

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

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

3. Assertion is correct but Reason is incorrect

4. Assertion is incorrect but Reason is correct.

Q. Find the lateral surface area and the total surface area of a solid cylinder of height 14 cm, if its volume is $686\pi c{m}^3$

1. 
   CSA= $614c{m}^2$ and TSA= $756c{m}^2$
2. 
   CSA= $616c{m}^2$ and TSA= $924c{m}^2$
3. 
   CSA= $233c{m}^2$ and TSA= $798c{m}^2$
4. 
   CSA= $614c{m}^2$ and TSA= $773c{m}^2$

Q.

Question 5 (ii)
It costs Rs. 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of $Rs20per{m}^2$, find:

(ii) The radius of the base.

Q. Question 2
The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost of whitewashing the walls of the room and ceiling at the rate of $Rs7.50per{m}^2$.

Q.

The tank of a tanker truck is a stainless steel cylinder. Find the surface area of the tank.

Q.

If each edge of a cube is doubled, how many times will its surface area increase?

Q.

Find the length of the side of a cube whose total surface area is $1536c{m}^2$.

1. $0.16m$

2. $0.16cm$

3. $1.6m$

4. $160cm$

Q. An oil tin in the shape of a cuboid has dimensions, 26 cm $\times$ 26 cm $\times$ 45 cm . If 1 sq. m sheet costs ₹10 , then the total cost for making 20 such tins is ____.

1. ₹120.64
2. ₹125.60
3. ₹128.60
4. ₹129.60

Q.

Diagonal of a cuboid of dimensions $l\times b\times h$ is _____________.

Q. Find the length of the longest pole that can be placed in a room 12 m long, 8 m broad and 9 m high.

Q. The length and breadth of a hall are in the ratio 4 : 3 and its height is 5.5 metres. The cost of decorating its walls (including doors and windows) at Rs 6.60 per square metre is Rs 5082. Find the length and breadth of the room.