Tag: volume of cylinder

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Multiple choice maths area and volume of cylinder hollow cylinder volume of cylinder 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 ${cm}^3\  \text{and}\ {cm}^2$)

  1. $1cm$
  2. $2cm$
  3. $3cm$
  4. $4cm$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Let radius of sphere be $'r'㎝$, then
TSA of sphere=volume of sphere
$\Rightarrow 4\pi { r }^{ 2 }=\cfrac { 4 }{ 3 } \pi { r }^{ 3 }\Rightarrow r=3cm$
Multiple choice maths area and volume of cylinder hollow cylinder volume of cylinder volume of cylinder and cone

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:

  1. $5\ \pi{R}^2$
  2. $4\ \pi{R}^2$
  3. $3\ \pi{R}^2$
  4. $2\ \pi{R}^2$
Reveal answer Fill a bubble to check yourself
D Correct answer
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$=6\pi { R }^{ 2 }-4\pi { R }^{ 2 }=2\pi { R }^{ 2 }$