Volume of a cuboid

Q. Question 4
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 by 10 cm by 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.

Q. The paint in a certain container is sufficient to paint an area of 9.375 mt sq. how many bricks measuring 22.5 cm * 10 cm *7.5 cm can be painted out of the paint in the container ?

Q. Jack has a toy in which half of the cylindrical shape is surmounted on a cuboid as shown in the figure below.

Total volume of the given solid is

1. $365.71c{m}^3$
2. $302.855c{m}^3$
3. $302.855c{m}^3$

Q.

Paul wants to put 1200 steel ball bearings (which are spherical in shape) with a radius of 5 mm, into a cylindrical container which is 30 cm high and 18 cm in diameter. Will all the bearings fit into the container?

Q. How many cubic centimetres of iron is required to construct an open box whose external dimensions are 36 cm, 25 cm and 16.5 cm provided the thickness of the iron is 1.5 cm. If one cubic cm of iron weighs 7.5 g, find the weight of the box.

Q. Find the area of the fields shown in Fig. (All measurements are in metres)

1. $2572m^2$
2. $25070m^2$
3. $2472m^2$
4. $2470m^2$

Q. Jack has a toy in which half of the cylindrical shape is surmounted on a cuboid as shown in the figure below.

Total volume of the given solid is

1. $365.71c{m}^3$
2. $302.855c{m}^3$
3. $302.855c{m}^3$

Q. the iron tank has length 5m and width 4 m and it contains 50 cm cube of water a small model tank is made and its value is 400 cm cube find the height of the model tank

Q. A solid iron cuboidal block of dimensions $4.4m\times 2.6m\times 1m$ is recasted into a hollow cylindrical pipe of internal radius $30cm$ and thickness $5cm$. Find the length of the pipe.

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. Length of the object

4. The space occupied by the object

Q. Earth dug out on digging a circular tank of diameter 17.5 m is spread all around the tank uniformly to a width of 4 m to from an embankment of height 2 m.
Calculate the depth of the circular tank correct upto two decimal places .

Q.

The volume of a cuboid is 1536 cube m. Its length is 16 m, and its breadth and height are in the ratio 3:2. Find the breadth and height of the cuboid.
(2 Marks)

Q. The total surface area of a solid cylinder is 616 $c{m}^2.$

Q. The volume of a cylinder is $448\pi c{m}^3$ and height is $7$ cm The lateral surface area of cylinder is

1. $252$ $c{m}^2$
2. $300$ $c{m}^2$
3. $352$ $c{m}^2$
4. $400$ $c{m}^2$

Q. A glass with diameter 20 cm has water to a height of 9 cm . A metal cube of 8 cm edge is immersed in it completely. calculate the height by which water will rise in the cylinder . (take $\pi =3.412)$

Q.

A building is in the form of a cuboid with an overhead tank in the form of a cylinder such that the tank spans halfway across the length of the building. Find the volume of the entire structure if the dimensions of the building is $20m\times 10m\times 20m$ and the height of the tank is 5m.

1. $4000+500\pi$

2. $4000+125\pi$

3. $4000+250\pi$

4. $4400+250\pi$

Q. If a well of height 20 m and diameter 7 m is dug out and the sand extracted from it is used to make a cuboid platform of length 14 m, breadth 22 m, then what is the height of the platform?

1. 10 m
2. 1 m
3. 2.5 m
4. 3.5 m

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 by 10 cm by 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 .

Q.

1. $75c{m}^3$
2. $70c{m}^3$
3. $100c{m}^3$
4. None of these

Q. Find the minimum length in cm and correct to nearest whole number of the thin metal sheet required to make a hollow and closed cylindrical box of diameter $20$ cm and height $35$ cm. Given that the width of the metal sheet is $1$ m. Also, find the cost of the sheet at the rate of Rs. $56$ per m. Find the area of metal sheet required, if $10\%$ of it is wasted in cutting, overlapping, etc.

1. $18cm$ and Rs. $15.68$ ; $3,111$ $c{m}^2$
2. $28cm$ and Rs. $15.68$ ; $3,111$ $c{m}^2$
3. $38cm$ and Rs. $15.68$ ; $3,111$ $c{m}^2$
4. $48cm$ and Rs. $15.68$ ; $3,111$ $c{m}^2$

Q. Jack has a toy in which half of the cylindrical shape is surmounted on a cuboid as shown in the figure below.

Total volume of the given solid is

1. $302.855c{m}^3$
2. $365.71c{m}^3$
3. $302.855c{m}^3$

Q.

A building is in the form of a cuboid with an overhead tank in the form of a cylinder such that the tank spans halfway across the length of the building. Find the volume of the entire structure if the dimensions of the building is $20m\times 10m\times 20m$ and the height of the tank is 5m.

1. $4000+500\pi$

2. $4000+125\pi$

3. $4000+250\pi$

4. $4400+250\pi$

Q. Jack has a toy in which half of the cylindrical shape is surmounted on a cuboid as shown in the figure below.

Total volume of the given solid is

1. $365.71c{m}^3$
2. $302.855c{m}^3$
3. $302.855c{m}^3$

Q. How much canvas is required to make a tent of base area $440$ sq metres and height $12$ metres?