Surface Area of Hollow Cylinder

Q.

The radius and height of a cylinder are increased by $10\%$, then what will be the percentage increase in volume?

Q.

A factory manufactures 120000 pencils daily. The pencils are cylindrical in shape each of length 25 cm and circumference of base as 1.5 cm. Determine the cost of colouring the curved surfaces of the pencils manufactured in one day at $Rs0.05perd{m}^2$.

Q.

A solid iron pole consists of a cylinder of height $220cm$ and base diameter$24cm,$ which is surmounted by another cylinder of height$60cm$ and radius $8cm.$ Find the mass of the pole, given that$1c{m}^3$ of iron has approximately $8g$ mass.

Q.

The difference between the outer and inner curved surface area of a hollow right circular cylinder 14 cm long is 88 $c{m}^2$. If the volume of metal used in making the cylinder is 176 $c{m}^3$, find the outer and inner diameters of the cylinder.

Q.

The decorative block shown in Fig. is made of two solids - a cube and a hemisphere. The base of the block is a cube with edge 5 cm, and the hemisphere fixed on the top has a diameter of 4.2 cm. Find the total surface area of the block. (Take $\pi =\frac{22}{7}$) [2 MARKS]

Q.

Question 8
The number of planks of dimensions $(4m\times 50cm\times 20cm)$ that can be stored in a pit which is 16 m long, 12 m wide and 4 m deep is:

A) 1900
B) 1920
C) 1800
D) 1840

Q.

The difference between the inner surface area and the outer surface area of a hollow cylinder having height 7 cm and inner and outer radius of 3 cm and 4 cm respectively is:

1. $22c{m}^2$
   

2. $44c{m}^2$
   

3. $88c{m}^2$
   

4. $42c{m}^2$

Q.

Sergio has two similar cylindrical pots, Pot $A$and Pot $B$. The radius of Pot $A$ is $15$ inches, and the radius of Pot $B$ is $3$ inches. What is the ratio of the volume of Pot $A$ to the volume of Pot $B$?

1. $10:1$

2. $25:1$

3. $125:1$

4. $5:1$

Q.

The cost of painting outer curved surface of a hollow hemispherical iron ball at rate of Rs. 2 per cm square is Rs. 1256. If thickness of the iron is 1 cm, find the cost of painting the inner curved surface of the ball.(Take $\pi$ = 3.14).

1. Rs. 2034.72

2. Rs. 1076.32

3. Rs. 1017.36

4. Rs. 508.68

Q.

A cylindrical saline bottle is injected into the vein of a patient. The saline bottle has radius 7 cm and height 20 cm. If the saline is released at a rate of 10 ${cm}^3$ per second, in approximately how many hours does the saline bottle gets emptied?

Q.

There is a hollow cylinder as shown in the figure having outer radius 7 cm, height 21 cm and inner radius 6 cm, whose inner and outer surfaces are to be painted. Calculate the area to be painted.

1. $792c{m}^2$
   

2. $924c{m}^2$
   

3. $1716c{m}^2$
   
   

4. $132c{m}^2$

Q.

The formula for the lateral surface area of a cylinder is $\mathrm{S}=2\mathrm{\pi rh}$ , where $r$ is the radius of the bases and $h$ is the height.

Solve for $h$.

1. $h=\frac{r}{2S\pi }$

2. $h=2S\pi r$

3. $h=\frac{S}{2\pi r}$

4. $h=\frac{Sr}{2\mathrm{\pi }}$

Q.

An iron cylinder of radius $1.4cm$and length $8cm$is found to weigh $369.6g$. Calculate the density of iron.

Q. Question 1
Write ‘True’ or ‘False’ and justify your answer in the following :
Two identical solid hemispheres of equal base radius r cm are stuck together along their bases. The total surface area of the combination $6\pi r^2$.

Q.

A big iron boiler tank opened on top is cylindrical in shape. It's height is $10$ m and radius is $7$ m. It gets corroded at a rate of $3$ sq. meter/day. The number of days in which it totally gets corroded is $(\text{Take}\pi =\frac{22}{7})$

1. 192

2. 202

3. 198

4. 208

Q. A vessel is in the form of hemispherical bowl surmounted by a hollow cylinder of same diameter. The diameter of the hemispherical bowl is $14cm$ and the total height of the vessel is $13cm$. Find the total surface area of the vessel. $[Use\pi =\frac{22}{7}]$

Q. The curved surface area of a right circular cylinder of height 14 cm is 88 cm${}^2$. Find the diameter of the base of the cylinder.

Q.

Find the distance between the two numbers
2.7 and 5.9

Q.

A solid cylinder of radius $r$ and height $h$ is placed over another cylinder of the same height and radius. The total surface area of the shape so formed is:

1. $4\mathrm{\pi rh}$

2. $4\mathrm{\pi rh}+2{\mathrm{\pi r}}^2$

3. $\mathrm{\pi rh}+{\mathrm{\pi r}}^2$

4. none of these

Q. A right circular cylinder has a base radius of 14 cm and a height of 21 cm. Find its volume. $[use\pi =\frac{22}{7}]$

1. $3080c{m}^3$
2. $12936c{m}^3$
3. $616c{m}^3$
4. $1848c{m}^3$

Q. From a solid cylinder whose height is $2.4cm$ and diameter $1.4cm$, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to the nearest $c{m}^2$.

Q. The height of the hollow cylinder is $12cm$. Find the volume and surface area of a hollow cylinder with inner radius $2cm$ and outer radius $4cm.$

Q.

Raghu had to make a cylindrical aluminium tube. What is the area of the aluminium sheet he needs to make the tube if the tube has a length of 1m and base radius of 3.5cm? ($\pi =\frac{22}{7}$)

Q. The height of the hollow cylinder is $10cm$. What is the volume and surface area of a hollow cylinder with inner radius $3cm$ and outer radius $6cm$? (Use $\pi =3$).

Q.

The inner diameter of a cylindrical wooden pipe is $24cm$ and its outer diameter is $28cm.$ The length of the pipe is $35cm$.Find the mass of the pipe, if $1c{m}^3$of wood has a mass of $0.6g$.

Q.

A leaky faucet drips at the rate of $300mL$ $perhour$. How long will it take to fill a $10L$ container?

Q. A person wants to make a cylindrical box which is open from the top. If the height of that box is 10 cm and radius is 7 cm find the area of sheet which is required to make it

Q. The inner diameter of a circular well is $3.5$ m. It is $10$ m deep. Find its inner curved surface area

Q. There is a hollow cylinder as shown in the figure having outer radius 7 cm, height 21 cm and inner radius 6 cm, whose inner and outer surfaces are to be painted. Calculate the area to be painted.

Q. The total surface area of a solid cylinder is $462{cm}^2$. Its curved surface area is one-third of its total surface area. Find the volume of the cylinder.