Cuboid and Its Surface Area

Q.

The sum of length, breadth and height of a cuboid is 19 cm and its diagonal is 5$\sqrt{5}$ cm. Its surface area is

(a) 361 $c{m}^2$ (b) 125 $c{m}^2$ (c) 236 $c{m}^2$ (d) 486 $c{m}^2$

Q. Total surface area of a cuboid whose length, breadth and height is 5 cm, 4 cm and 3 cm, respectively, is .

1. $86{\text{cm}}^2$
2. $94{\text{cm}}^2$
3. $51{\text{cm}}^2$
4. $64{\text{cm}}^2$

Q.

From a solid cylinder of height 30 cm and radius 7 cm, a conical cavity of height 24 cm and of base radius 7 cm is drilled out. Find the volume and the total surface of the remaining solid. [4 MARKS]

Q.

From a rectangular solid of metal 42 cm by 30 cm by 20 cm, a conical cavity of diameter 14 cm and depth 24 cm is drilled out. Find :
(i) the surface area of remaining solid,
(ii) the volume of remaining solid,
(iii) the weight of the material drilled out if it weighs 7 gm per $c{m}^3$.

Q. Question 1
2 cubes each of volume 64 $c{m}^3$ are joined end to end. Find the surface area of the resulting cuboid.

Q.

A room is $6m$ long, $5m$ broad and $4m$ in height. If all its walls are to be covered with paper $50cm$ wide, the length of the paper is

Q.

The volume of a cube of ice for an ice sculpture is $64,000$ cubic inches.

What is the surface area of the cube of ice?

Q.

$2$cubes each of volume$64{\mathrm{cm}}^3$ are joined end to end. Find the surface area of the resulting cuboid.

Q. Total surface area of a cuboid whose length, breadth and height is 5 cm, 4 cm and 3 cm, respectively, is .

1. $51{\text{cm}}^2$
2. $86{\text{cm}}^2$
3. $94{\text{cm}}^2$
4. $64{\text{cm}}^2$

Q.

A small indoor greenhouse (herbarium) is made entirely of glass panes (including base) held together with tape.

It is $30cm$ long, $25cm$ wide and $25cm$ high.

1. What is the area of the glass?
2. How much of tape is needed for all the $12$ edges?

Q.

The length of the longest pole that can be kept in a room $(12m\times 9m\times 8m)$ is

(a) 29 m (b) 21 m (c) 19 m (d) 17 m

Q.

A rectangular cardboard of dimension 20 m $\times$ 10 m is placed on a table. 4 squares of side 2.5 m are cut out from the corners and the 4 sides are folded . Find the surface area of the resulting figure which is to be painted on all the sides.

1. 175 $m^2$

2. 155 $m^2$
3. 180 $m^2$
4. 100 $m^2$

Q. The total surface area of a cuboid with dimensions of $26\times 14\times 6.5$ m respectively is _____ m${}^2$.

1. 1248
2. 1448
3. 1000
4. 2400

Q.

The dimensions of a room are $14m\times 10m\times 6.5m$.There are two doors and 4 windows in the room.Each door measures $2.5m\times 1.2m$ and window measures $1.5m\times 1m$.Find the cost of painting walls of the room ar Rs.35 per $m^2$.

Q. A box made up of tin sheets measures length 9 m, breadth 2 m and height 3.5 m. Then maximum number of cubical cartons of edge 0.5 m be stored in the box is

1. 1000
2. 1200
3. 504
4. 500

Q.

Three cubes of side $4cm$ each, are joined end to end. Then, the total surface area of the resultant cuboid is

1. $224c{m}^2$

2. $124c{m}^2$

3. $220c{m}^2$

4. None of these

Q. The dimensions of a cuboid are 35 cm × 30 cm × 25 cm. If Amit cuts a cube of greatest volume, then the volume of the cube is

1. $42875c{m}^3$
2. $15625c{m}^3$
3. $27000c{m}^3$
4. $3375c{m}^3$

Q. Total surface area of a cuboid whose length, breadth and height is 5 cm, 4 cm and 3 cm, respectively, is .

1. $86{\text{cm}}^2$
2. $94{\text{cm}}^2$
3. $51{\text{cm}}^2$
4. $64{\text{cm}}^2$

Q. Water in a canal, 4 m wide and 15 m deep is flowing with the speed of 12 km/h. Then the area of field it will irrigate in 20 minutes, if 10 cm of standing water is required for irrigation, is

1. $4000000m^2$
2. $2400000m^2$
3. $2500000m^2$
4. $5000000m^2$

Q.

What is the importance of finding areas and perimeters of circular shapes?

Q. What is the total surface area of a room (cuboidal in shape) of length $12ft$, breadth $10ft$, and height $8ft$?

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.

What do you understand by the quantity called ‘area’?

1. It is the quantity of an object

2. It is the length of an object

3. It is the quantity that expresses the extent of a planar 2-D surface

4. It is the height of an object

Q.

The dimensions of a godown are $40\mathrm{m},25\mathrm{m}\mathrm{and}10\mathrm{m}$. If it is filled with cuboidal boxes each of dimensions $2\mathrm{m}\times 1.25\mathrm{m}\times 1\mathrm{m}$, then the number of boxes will be

1. $1800$

2. $2000$

3. $4000$

4. $8000$

Q. Question 20
A pen stand made of wood is in the shape of a cuboid with four conical depressions and a cubical depression to hold the pens and pins, respectively. The dimension of the cuboid are 10 cm, 5 cm and 4 cm. The radius of each of the conical depressions is 0.5 cm and the depth is 2.1 cm. The edge of the cubical depression is 3 cm. Find the volume of the wood in the entire stand.

Q.

Water in a canal, $5.4\mathrm{m}$ wide and $1.8\mathrm{m}$ deep, is flowing with a speed of $25\mathrm{km}/\mathrm{hour}$. How much area can it irrigate in $40\mathrm{minutes}$, if $10\mathrm{cm}$ of standing water is required for irrigation

Q.

Basic of circumference and area explain

Q.

A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm × 10 cm × 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand.

1. 550 $c{m}^3$

2. 456.89 $c{m}^3$

3. 576.63 $c{m}^3$

4. 523.53 $c{m}^3$

Q.

An open metal bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet (see Fig.). The diameters of the two circular ends of the bucket are 45 cm and 25 cm, the total vertical height of the bucket is 40 cm and that of the cylindrical base is 6 cm. Find the area of the metallic sheet used to make the bucket, where we do not take into account the handle of the bucket. Also, find the volume of water the bucket can hold. (Take $\pi =\frac{22}{7}$) [4 MARKS]

Q. A surface has
(a) 0 dimension
(b) 1 dimension
(c) 2 dimensions
(d) 3 dimensions