Tag: volume of cylinder and cone

Questions Related to volume of cylinder and cone

The value of radius for which the numerical value of total surface area of a sphere and the volume of sphere are equal, will be:(Consider the units of volume and surface area as ${cm}^3\  \text{and}\ {cm}^2$)

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

  1. $1cm$

  2. $2cm$

  3. $3cm$

  4. $4cm$

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Correct Option: C
Explanation:
Let radius of sphere be $'r'㎝$, then
TSA of sphere=volume of sphere
$\Rightarrow 4\pi { r }^{ 2 }=\cfrac { 4 }{ 3 } \pi { r }^{ 3 }\Rightarrow r=3cm$

The increase in the total surface area of a sphere of Radius ${R}$ when it is cut to make two hemispheres of same Radius will be equal to:

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

  1. $5\ \pi{R}^2$

  2. $4\ \pi{R}^2$

  3. $3\ \pi{R}^2$

  4. $2\ \pi{R}^2$

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Correct Option: D
Explanation:
Total surface area of sphere$=4\pi { R }^{ 2 }$
TSA of hemisphere=CSA of hemisphere+CSA of circle
$=2\pi { R }^{ 2 }+\pi { R }^{ 2 }=3\pi { R }^{ 2 }$
$\therefore $TSA of two hemisphere$=2\times 3\pi { R }^{ 2 }=6\pi { R }^{ 2 }$
Therefore, increase in TSA$=6\pi { R }^{ 2 }-4\pi { R }^{ 2 }=2\pi { R }^{ 2 }$

The height of a cylinder is  $14 { cm }$  and its  $ { CSA }$  is  $264 { cm } ^ { 2 },$  then cylinder is.........${ cm }^{ { 3 } }$

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

  1. $183$

  2. $396$

  3. $896$

  4. $968$

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Correct Option: A