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Questions Related to maths

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

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

  1. $224\, \pi\, cm^{2}$
  2. $212\, \pi\, cm^{2}$
  3. $112\, \pi\, cm^{2}$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
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 $

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

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

  1. $3.6 kg$
  2. $3.696 kg$
  3. $36 kg$
  4. $36.9 kg$
Reveal answer Fill a bubble to check yourself
B Correct answer
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$
Multiple choice maths area and volume of cylinder hollow cylinder volume of cylinder volume of cylinder and cone

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

  1. $\displaystyle \frac { 22 }{ 49 } $
  2. $\displaystyle \frac { 44 }{ 29 } $
  3. $\displaystyle \frac { 49 }{ 22 } $

  4. None
Reveal answer Fill a bubble to check yourself
C Correct answer
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}$

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

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

  1. remain same

  2. increase

  3. decrease

  4. none of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
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

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

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?

  1. $\displaystyle 2.1\pi$ litres
  2. $\displaystyle 2.25\pi$ litres
  3. $\displaystyle 225\pi$ litres
  4. $\displaystyle 2250\pi$ litres
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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

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

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

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$^2$.

  1. Rs. $4000$
  2. Rs. $4400$
  3. Rs. $4500$
  4. Rs. $4800$
Reveal answer Fill a bubble to check yourself
B Correct answer
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. $4400$.

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

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

  1. $231{ cm }^{ 2 }$
  2. $154{ cm }^{ 2 }$
  3. $308{ cm }^{ 2 }$
  4. $115.5{ cm }^{ 2 }$
Reveal answer Fill a bubble to check yourself
A Correct answer
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 $=231cm^2$.

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

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 $Rs.10$

  1. $Rs.950$
  2. $Rs.945$
  3. $Rs.942$
  4. $Rs.1000$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Surface area of a ring-shaped magnet (hollow cylinder) includes inner CSA, outer CSA, and two annular ends. Inner r=2, outer R=3, h=2. Area = 2*pi*r*h + 2*pi*R*h + 2*(pi*R^2 - pi*r^2) = 2*pi*2*2 + 2*pi*3*2 + 2*pi*(9-4) = 8*pi + 12*pi + 10*pi = 30*pi. 30 * 3.14 = 94.2. Cost = 94.2 * 10 = 942.

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

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 $Rs.2$.

  1. $Rs.276.32$
  2. $Rs.275$
  3. $Rs.270$
  4. $Rs.278.64$
Reveal answer Fill a bubble to check yourself
A Correct answer
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 $==138.16\times 2=Rs.276.32$

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

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)

  1. $706.86\ {cm^2}$
  2. $804.25\ {cm^2}$
  3. $2827.43\ {cm^2}$
  4. $3216.99\ {cm^2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Inner surface area of a spherical shell = 4 * pi * r^2. With r = 15, Area = 4 * 3.14159 * 225 = 2827.43 cm^2.