Tag: maths

Questions Related to maths

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

maths area and volume of cylinder hollow cylinder volume of cylinder volume of cylinder and cone

  1. $224\, \pi\, cm^{2}$

  2. $212\, \pi\, cm^{2}$

  3. $112\, \pi\, cm^{2}$

  4. None of these

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Correct Option: C
Explanation:

Volume of a Cylinder of Radius $R$ and height $h$ $ = \pi { R }^{ 2 }h $
$\therefore $ volume of the given cylinder $ =\pi \times {R}^{2} \times 7  = 448 \pi  {cm}^{3} $

$ {R}^{2} = 64 $

$ R = 8 cm $  

Curved surface area of a cylinder of radius "$R$" and height "$h$" $ = 2\pi Rh$

$\therefore$ curved surface area of the given cylinder $ = 2\times \pi \times 8\times 7 =  112 \pi   \  cm^2 $

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

maths area and volume of cylinder hollow cylinder volume of cylinder volume of cylinder and cone

  1. $3.6 kg$

  2. $3.696 kg$

  3. $36 kg$

  4. $36.9 kg$

Show answer
Correct Option: B
Explanation:
Let external diameter be ${ d } _{ 2 }$ and internal be ${ d } _{ 1 }$
$\Rightarrow { d } _{ 2 }=8cm$ & ${ d } _{ 1 }=8-1-1=6cm$
Therefore, ${ r } _{ 1 }=3cm$ & ${ r } _{ 2 }=4cm$
Volume of hollow cylindrical pipe$=\pi \left( { r } _{ 2 }^{ 2 }-{ r } _{ 1 }^{ 2 } \right) \times h$
$=\cfrac { 22 }{ 7 } \left( { \left( 4 \right)  }^{ 2 }-{ \left( 3 \right)  }^{ 2 } \right) \times 21$
$=\cfrac { 22 }{ 7 } \times 7\times 21$
$=462cm^3$
$\therefore $Weight of the pipe$=8\times 462=3696g=3.696kg$

A rectangular sheet of width $14$ m is rolled along its width and is converted to form a cylinder. Find the radius of cylinder.

maths area and volume of cylinder hollow cylinder volume of cylinder volume of cylinder and cone

  1. $\displaystyle \frac { 22 }{ 49 } $

  2. $\displaystyle \frac { 44 }{ 29 } $

  3. $\displaystyle \frac { 49 }{ 22 } $

  4. None

Show answer
Correct Option: C
Explanation:

Curved surface area of cylinder$=100m^2$

$\therefore 2 \pi r h = 100$
Here, width of the rectangle = height of the cylinder.
$\therefore h=14m$

$\therefore 2 \times \dfrac {22}{7} \times r \times 14 = 100$

$ \therefore r = \dfrac {100 \times 7}{2 \times 22 \times 14}$

In a cylinder, if the radius is halved and height is doubled, the curved surface area will 

maths area and volume of cylinder hollow cylinder volume of cylinder volume of cylinder and cone

  1. remain same

  2. increase

  3. decrease

  4. none of the above

Show answer
Correct Option: A
Explanation:

Volume of cylinder $\displaystyle \pi { r }^{ 2 }h$
Now, if $\displaystyle r=\frac { r }{ 2 } & h=h2$
New CSA $\displaystyle =2\pi rh$
$\displaystyle =2\pi \left( \frac { r }{ 2 }  \right) \times \left( h\times 2 \right) $
$\displaystyle =2\pi rh$
It will remain same

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?

maths area and volume of cylinder hollow cylinder volume of cylinder volume of cylinder and cone

  1. $\displaystyle 2.1\pi$ litres

  2. $\displaystyle 2.25\pi$ litres

  3. $\displaystyle 225\pi$ litres

  4. $\displaystyle 2250\pi$ litres

Show answer
Correct Option: B
Explanation:

Circumference $\displaystyle 2\pi r=30\pi ,r=\frac { 30\pi  }{ 2\pi  } =15$

Volume of cylinder $\displaystyle =\pi { r }^{ 2 }h$
$\displaystyle =\left( \pi \times 10\times 15\times 15 \right) { cm }^{ 3 }$
$\displaystyle =2250\pi { cm }^{ 3 }$
$\displaystyle =2.25\pi l$

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$^2$.

maths area and volume of cylinder hollow cylinder volume of cylinder volume of cylinder and cone

  1. Rs. $4000$

  2. Rs. $4400$

  3. Rs. $4500$

  4. Rs. $4800$

Show answer
Correct Option: B
Explanation:

Given diameter of well is $3.5$ m and depth is $10$ m and cost of plastering is Rs. $40$ per sq m.

Then radius of well $=\dfrac{3.5}{2}=1.75$ m
And height of well $=10$ m
Then curved surface area of well $=$ $2\pi rh=2\times \dfrac{22}{7}\times 1.75\times 10$
$=$ $2\times 22\times 0.25\times 10=110 m^{2}$
Then cost of plastering curved surface area $=$ $110\times 40=$ Rs. $4400$.

The height of a hollow cylinder is $7 cm$ and its radius is $3.5 cm$. Then the surface area is

maths area and volume of cylinder hollow cylinder volume of cylinder volume of cylinder and cone

  1. $231{ cm }^{ 2 }$

  2. $154{ cm }^{ 2 }$

  3. $308{ cm }^{ 2 }$

  4. $115.5{ cm }^{ 2 }$

Show answer
Correct Option: A
Explanation:

Given : radius $r=3.5 cm$ and height $h=7cm$

Surface area of a hollow cylinder $=2\pi r(h+r)$
                                                        $=2\times 3.14\times 3.5(7+3.5)$
                                                        $=230.79cm^2\approx 231$
$\therefore$ Surface area $=231cm^2$.

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 $Rs.10$

maths area and volume of cylinder hollow cylinder volume of cylinder volume of cylinder and cone

  1. $Rs.950$

  2. $Rs.945$

  3. $Rs.942$

  4. $Rs.1000$

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Correct Option: C

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 $Rs.2$.

maths area and volume of cylinder hollow cylinder volume of cylinder volume of cylinder and cone

  1. $Rs.276.32$

  2. $Rs.275$

  3. $Rs.270$

  4. $Rs.278.64$

Show answer
Correct Option: A
Explanation:

We have to first find the total surface area of the flower pot.
Outer radius $=4cm$
Inner radius $=2cm$
Height of flower pot $=10cm$
Total surface area $=A=2\pi Rh+2\pi rh+\pi { { R }^{ 2 } }+\pi { { r }^{ 2 } }$
$A=2\pi (R+r)h+\pi ({ R }^{ 2 }+{ r }^{ 2 })\ A=2\pi (4+2)2+\pi (16+4)\ A=24\pi +20\pi =44\pi \ A=40\pi =44\times 3.14=138.16{ cm }^{ 2 }$
Cost of fabrication per ${cm}^{2}$ $=Rs.2$
Total cost of fabrication $==138.16\times 2=Rs.276.32$

What will be the Inner surface area of a spherical shell of inner radius $15\ cm$ and outer radius $16\ cm$? (Correct upto 2 decimal places)

maths area and volume of cylinder hollow cylinder volume of cylinder volume of cylinder and cone

  1. $706.86\ {cm^2}$

  2. $804.25\ {cm^2}$

  3. $2827.43\ {cm^2}$

  4. $3216.99\ {cm^2}$

Show answer
Correct Option: C