Questions
The volume, V $cm^{2}$, of a hollow cylindrical pipe of length $l$ cm, outer radius R cm and inner radius r cm is given by the formula : $V, =, \pi, (R^{2}, -, r^{2})., l$
- 1.5
- 1.2
- 1.4
- 1.6
An iron pipe $20\space cm$ long has exterior diameter equal to $25\space cm$. If the thickness of the pipe is $1\space cm$, find the whole surface area of the pipe.
- $3167\space cm^2$
- $3160\space cm^2$
- $3068\space cm^2$
- $3268\space cm^2$
The diameters of two cylinders are in the ratio of 2:1 and their volumes are equal. The ratio of their heights will be _________.
- 1:6
- 1:2
- 1:4
- 3:4
If the volume of a cylinder is $448\pi:cm^3$ and height 7 cm, its total surface area will be ______________.
- $352:cm^2$
- $754.28:cm^2$
- $724.64:cm^2$
- $354:cm^2$
A rectangular paper of dimensions 6 cm and 3 cm is rolled to form a cylinder with height equal to the width of the paper, then its base radius is
- $ \displaystyle \frac{6}{\pi }cm $
- $ \displaystyle \frac{3}{2\pi }cm $
- $ \displaystyle \frac{6}{2\pi }cm $
- $ \displaystyle \frac{9}{2\pi }cm $
The curved surface of a circular cylinder of height 'h' and the curved surface area of the cone of slant height 2 'h' having the same circular base are in the ratio of
- 1 : 2
- 2 : 1
- 1 : 1
- 1 : 3
A hollow sphere of internal and external radii 3 cm and 4 cm respectively is malted into a cylinder of diameter 37 cm The height of the cylinder is
- 2 cm
- 2.5 cm
- 3 cm
- none
The outer and inner diameters of a circular pipe are $6$ cm and $4$ cm respectively. If its length is $10$ cm then what is the total surface area in square centimetres?
- $55\pi$
- $110\pi$
- $150\pi$
- None of the above
A test-tube consists of a hollow cylindrical tube joined to a hemi-spherical bown of the same internal radius. The whole tube holds $350$ cc of water and in the cylindrical portion falls $1$ cm if $19.64$ cc of water is removed. Find the length of the cylindrical portion of the tube. (Take $\pi =$ $22/7$)
- $12.15$ cm
- $16.15 $ cm
- $24.15 $ cm
- None of these
The height of a hollow cylinder is $14cm$ if external diameter is $16cm$ and total curved surface area of the hollow cylinder is $1320sq.cm$, then its internal diameter is
- $14cm$
- $16cm$
- $7cm$
- $8cm$
The ratio between the radius of the base and the height of a cylinder is $2:3$. If its volume is $12936$ cu. cm, the total surface area of the cylinder is :
- $2587.2 c{m^2}$
- $3080 c{m^2}$
- $25872 c{m^2}$
- $38808 c{m^2}$
A cylinder and cone of equal base radius and equal height are given. Which of the following statement is true/
- Volume of cylinder and cone are equal
- Volume of cylinder is one-third of volume of cone
- Volume of cone is half of the volume of cylinder
- Volume of cone is one-third of volume of cylinder
Find the volume of a solid cylinder whose radius is $14$cm and height $30$cm
- $18380cm^3$
- $18480cm^3$
- $18580cm^3$
- $18680cm^3$
the radii of two cylinders are in the ratio 2:3 and their height are in the ratio 5:3. ratio of their volume
- $20:27$
- $10:9$
- $18:13$
- $9:20$
A solid cylinder has a total surface area of $231cm^2$. Its curved surface area. Find the volume of the cylinder?
- $270cm^3$
- $269.5cm^3$
- $256.5cm^3$
- $289.5cm^3$
Volume of a cylinder when $d=7\ cm$ and $h=3\ cm$
- $118\ cm^{3}$
- $115.5\ cm^{3}$
- $155.5\ cm^{3}$
- $808.5\ cm^{3}$
A cylindrical pipe is made from a metal sheet of length 88 cm and breadth 20 cm. What is the volume of this pipe?
- $2800$ ${ cm }^{ 3 }$
- $12320$ ${ cm }^{ 3 }$
- $13202$ ${ cm }^{ 3 }$
- $13220$ ${ cm }^{ 3 }$
If sum of radius and height of a cylinder is 6, then its maximum volume is
- $32\pi$
- $16\pi$
- $8\pi$
- None of these
Mark the correct alternative of the following.
Two cylindrical jars have their diameters in the ratio $3:1$, but height $1:3$. Then the ratio of their volumes is?
- $1:4$
- $1:3$
- $3:1$
- $2:5$
Mark the correct alternative of the following.
In a cylinder, if radius is doubled and height is halved, curved surface area will be?
- Halved
- Doubled
- Same
- Four times
Mark the correct alternative of the following.
The radius of a wire is decreased to one-third. If volume remains the same, the length will become?
- $3$ times
- $6$ times
- $9$ times
- $27$ times
Mark the correct alternative of the following.
If the height of a cylinder is doubled and radius remains the same, then volume will be?
- Doubled
- Halved
- Same
- Four times
Mark the correct alternative of the following.
In a cylinder, if radius is halved and height is doubled, the volume will be?
- Same
- Doubled
- Halved
- Four times
Mark the correct alternative of the following.
If the radius of a cylinder is doubled and the height remains same, the volume will be?
- Doubled
- Halved
- Same
- Four times
Mark the correct alternative of the following.
The volume of a cylinder of radius r is $1/4$ of the volume of a rectangular box with a square base of side length x. If the cylinder and the box have equal heights, what is r in terms of x?
- $\dfrac{x^2}{2\pi}$
- $\dfrac{x}{2\sqrt{\pi}}$
- $\dfrac{\sqrt{2x}}{\pi}$
- $\dfrac{\pi}{2\sqrt{x}}$
Mark the correct alternative of the following.
Two circular cylinders of equal volume have their heights in the ratio $1:2$. Ratio of their radii is?
- $1:\sqrt{2}$
- $\sqrt{2}:1$
- $1:2$
- $1:4$
Mark the correct alternative of the following.
The altitude of a right circular cylinder is increased six times and the base area is decreased one-ninth of its value. The factor by which the lateral surface of the cylinder increases, is?
- $\dfrac{2}{3}$
- $\dfrac{1}{2}$
- $\dfrac{3}{2}$
- $2$
Mark the correct alternative of the following.
The height h of a cylinder equal the circumference of the cylinder. In terms of h, what is the volume of the cylinder?
- $\dfrac{h^3}{4\pi}$
- $\dfrac{h^2}{2\pi}$
- $\dfrac{h^3}{2}$
- $\pi h^3$
A hollow cylindrical pipe is $21 \ cm$ long. If its outer and inner diameters are $10 \ cm$ and $6 \ cm$ respectively, them the volume of the metal used in making the pipe is $\displaystyle \left(Take, \pi, =, \frac{22}{7}\right)$
- $1048, cm^{3}$
- $1056, cm^{3}$
- $1060, cm^{3}$
- $1064, cm^{3}$
If the volume of a vessel in the form of a right circular cylinder is 448 $\pi, cm^{3}$ and its height is 7 cm, then the curved surface area of the cylinder is
- $224, \pi, cm^{2}$
- $212, \pi, cm^{2}$
- $112, \pi, cm^{2}$
- None of these
A hollow iron pipe of $21 cm$ long and its external diameter is $8 cm$. If the thickness of the pipes is $1 cm$ and iron weights $\displaystyle 8g/cm^{2}$, then the weight of the pipe is equal to
- $3.6 kg$
- $3.696 kg$
- $36 kg$
- $36.9 kg$
A rectangular sheet of width $14$ m is rolled along its width and is converted to form a cylinder. Find the radius of cylinder.
- $\displaystyle \frac { 22 }{ 49 } $
- $\displaystyle \frac { 44 }{ 29 } $
- $\displaystyle \frac { 49 }{ 22 } $
- None
In a cylinder, if the radius is halved and height is doubled, the curved surface area will
- remain same
- increase
- decrease
- none of the above
The circumference of base of cylindrical reservoir is $\displaystyle 30\pi cm$ and height is $10$ cm. How many litres of water can it hold?
- $\displaystyle 2.1\pi$ litres
- $\displaystyle 2.25\pi$ litres
- $\displaystyle 225\pi$ <span>litres</span>
- $\displaystyle 2250\pi$ <span>litres</span>
The inner diameter of a circular well is $3.5$ m. It is $10$ m deep. Find the cost of plastering this curved surface at the rate of Rs. $40$ per m$^2$.
- Rs. $4000$
- Rs. $4400$
- Rs. $4500$
- Rs. $4800$
The height of a hollow cylinder is $7 cm$ and its radius is $3.5 cm$. Then the surface area is
- $231{ cm }^{ 2 }$
- $154{ cm }^{ 2 }$
- $308{ cm }^{ 2 }$
- $115.5{ cm }^{ 2 }$
A magnet is in the form of a ring with inner diameter $4cm$ and outer diameter $6cm$. If the thickness of the magnet is $2cm$ . What is the cost of fabricating the surface of the magnet if the cost of fabrication per ${cm}^{2}$ is $Rs.10$
- $Rs.950$
- $Rs.945$
- $Rs.942$
- $Rs.1000$
A flower pot is in the form of a hollow cylinder with a closed base with inner radius $2cm$ and outer radius $4cm$ . The height of the flower pot is $10cm$ . If the pot has to be polished find the cost of polishing if the cost of polishing per ${cm}^{2}$ is $Rs.2$.
- $Rs.276.32$
- $Rs.275$
- $Rs.270$
- $Rs.278.64$
The height of a cylinder is $14 { cm }$ and its $ { CSA }$ is $264 { cm } ^ { 2 },$ then cylinder is.........${ cm }^{ { 3 } }$
- $183$
- $396$
- $896$
- $968$