Volume of a cuboid

Q.

What full form of CSA and TSA? Write the edge of cube in terms of its volume.

Q.

A cubical box has each edge$10cm$ and another cuboidal box is $12.5cm$ long, $10cm$wide and $8cm$ high (i) Which box has the greater lateral surface area and by how much? (ii) Which box has the smaller total surface area and by how much?

Q.

The paint in a certain container is sufficient to paint an area equal to $9.375{\mathrm{m}}^2$. How many bricks of dimensions $22.5\times 10\times 7.5\mathrm{cm}$ can be painted out of this container?

Q.

The water in a rectangular reservoir has a base $80m\times 60m$ and is $6.5m$ deep. In what time(in hours) can the water be emptied by a pipe having a cross section in the form of a square of side $20cm$, if water runs through the pipe at the rate of $15km/hr$?

1. $50$

2. $40$

3. $52$

4. $42$

Q. A rectangular form a cylinder of a vessel 25cm*8 cm*11cm is full of milk.If the milk is poured into an empty cylindrical vessel of diameter 20cm, what will be the height of milk in the vessel ?
Pls help me to solve this question.

Q.

A hollow cylindrical copper pipe is 21 dm long . Its outer and inner diameters are 10 cm and 6 cm respectively. Find the volume of the copper used in making the pipe

Q.

The dimensions of a cuboid are in the ratio $5:2:1$. Its volume is $1250$ cubic meters. Find the total surface area.

Q.

Find a formula for the described function. An open rectangular box with volume $4{\mathrm{m}}^3$ has a square base. Express the surface area $\mathrm{SA}$ of the box as a function of the length of a side of the base, $x$. $\mathrm{SA}=$${\mathrm{m}}^2$ State the domain of $\mathrm{SA}$. (Enter your answer in interval notation).

Q.

The paint in a container is sufficient to paint an area equal to $9.375m^2$. How many bricks of dimensions $22.5cm\times 10cm\times 7.5cm$ can be painted out of this container?

Q. Find the volume of a cuboid whose
$\left(ii\right).$ length $=1.2m$, breadth $=30cm$, height $=15cm$

Q.
Find the volume of the given solid if all the cubes are identical and have a side length of $3$ units.

1. 250 units${}^3$
2. 170 units${}^3$
3. 270 units${}^3$
4. 80 units${}^3$

Q. The ratio of surface area of a cube of volume 64 cm${}^3$ to that of 64 cubes of volume 1 cm${}^3$ each = .

1. 1:4
2. 1:1
3. 1:2

Q. Sixteen cylindrical cans each with a radius of $1$ unit are placed inside a cardboard box four in a row. If the cans touch the adjacent cans and or the walls of the box, then which of the following could be the interior area of the bottom of the box in square units?

1. $16$
2. $32$
3. $64$
4. $128$

Q. Find cube of $\frac{a^{\frac{1}{2}}\times b^{\frac{1}{5}}}{c^{\frac{1}{3}}\times d^2}$:

1. $\frac{a^{\frac{3}{2}}{b}^{\frac{3}{5}}}{c{d}^3}$
2. $\frac{a^{\frac{3}{2}}{b}^{\frac{1}{5}}}{c{d}^6}$
3. $\frac{a^{\frac{3}{2}}{b}^{\frac{1}{5}}}{c^{\frac{1}{3}}{d}^2}$
4. $\frac{a^{\frac{3}{2}}{b}^{\frac{3}{5}}}{c{d}^6}$

Q. Tick (✓) the correct answer:
A circular well with a diameter of 2 metres, is dug to a depth of 14 metres. What is the volume of the earth dug out?
(a) 32 m³
(b) 36 m³
(c) 40 m³
(d) 44 m³

Q.

To fill a 4 m wide, 8 m long and 3 m deep sand box, how much sand do you need?

1. 96 cubic metres

2. 150 cubic metres

3. 200 cubic metres

4. 32 cubic metres

Q. The area of a circle is 154 square centimeters. If the radius of the sphere is the same as the radius of the circle, then what will the volume of the sphere be?

(Note: $\pi =\frac{22}{7}$)

1. 1437.33 cu cm
2. 4312 cu cm
3. 205.33 cu cm
4. 1437.33 cu cm

Q. A solid cylinder has a total surface area of $462$ $c{m}^3$ Its curved surface area is one-third of its total surface area . The volume of the cylinder is :$(\pi =\frac{22}{7})$

1. $539$ $c{m}^3$
2. $792$ $c{m}^3$
3. $495$ $c{m}^3$
4. $676$ $c{m}^3$

Q. A cuboid is of dimensions $60cm\times 54cm\times 30cm$. How many cubes with side $6cm$ can be placed in the given cuboid?​

Q.

What is meant by the ‘volume’ of an object?

1. The weight of the object

2. The amount of substance it is composed of

3. The space occupied by the object

4. Length of the object

Q.

Water in a river 6m wide and 1.5m deep flows with a speed of 10km/hr. How much area will it irrigate in half an hour if 8cm of standing water is needed?

1. 52.45 Hectares

2. 49.25 Hectares

3. 56.25 Hectares

4. 66.76 Hectares

Q. Find the total cost to paint external areas of all the 4 walls of a room with length, breadth and height as 10 cm, 20 cm and 5 cm respectively at the rate of ₹10 per sq. metre.

Q. Mohan wanted to paint the walls and ceiling of a hall. The dimensions of the hall are $20m$ $\times$ $15m$ $\times$ $6m.$ Find the area of the surface to be painted and the cost of painting it at $Rs.78$ per square meter.

Q.

The dimensions of a cuboid are in the ratio of 1 : 2 : 3 and its Total surface area is 88 $m^2$. The volume of cuboid is___ $m^3$

Q. An ice cream cone has a depth of 90 cm and a radius of 20 cm, respectively. The volume of the cone ice cream is.

1. $4,000\pi c{m}^3$
2. $10,000\pi c{m}^3$
3. $3,000\pi c{m}^3$
4. $12,000\pi c{m}^3$

Q.

Find the volume of a cuboid of dimensions 20 × 10 × 5 units.

1. 100

2. 500

3. 1000

4. 1500

Q. Find the volume of the cuboid shown below.

1. $90,000m^3$
2. $45m^3$
3. $90m^3$
4. $45,000m^3$

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

1. Cuboid, MKN
2. Cuboid, 4MKN
3. Sphere, 4MKN
4. Cylinder, 2 MKN

Q. Shishir is making a larger cube of side 6 cm using cubes of side 2 cm. How many such cubes are needed?

1. 9
2. 27
3. 36
4. 216

Q. A store room in the form of a cuboid has dimensions $42m\times 35m\times 21m.$ How many cuboidal boxes can be stored in it if the volume of each box is $0.7m^3?$

1. 30870
2. 44000
3. 44100
4. 4200