Volume and Surface Area Questions Answers Formulas, Tips and Tricks

• 1. Formula of Cuboid Volume, Surface Area and Daigonal

  
  

  Let l be length, b be breadth and height = h units then,
  
  \begin{aligned}
  \text{Volume of Cuboid =}(l*b*h)\text{cubic units} \\
  \text{Surface Area} = 2(lb + bh +hl)\text{sq. units}\\
  \text{Diagonal =}\sqrt{l^2+b^2+h^2} units
  
  \end{aligned}

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• 2. Formula of Cube Volume, Surface Area and Diagonal

  
  

  Let each edge of a cube be of length a, then
  \begin{aligned}
  \text{Volume of cube =} a^3 \\
  \text{Surface Area of cube =} 6a^2 &sq.units \\
  \text{Diagonal of cube =} \sqrt{3}a & units\\
  \end{aligned}

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• 3. Cylinder Volume, Curved Surface Area, Total Surface Area Formula

  
  

  \begin{aligned}
  \text{Volume of cylinder =} (\pi r^2 h)\text{cubic units} \\
  
  \text{Curved surface area of cylinder =} (2\pi r h) \text{sq. units}\\
  
  \text{Total surface area of cylinder =} (2\pi r h + 2 \pi r^2 ) \text{sq. units}\\
  = 2 \pi r (h+r) \text{sq. units}
  
  \end{aligned}

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• 4. Cone Slant Height, Volume, Curved Surface Area, Total Surface Area Formula

  
  

  Let Radius of base = r and height = h. Then,
  \begin{aligned}
  \text{Slant Height of cone, l = }\sqrt{r^2+h^2} units \\
  \text{Volume of cone = }\left( \frac{1}{3}\pi r^2 h \right) \text{cubic units} \\
  
  \text{Curved surface area of cone = }\left( \pi rl \right) \text{sq. units} \\
  
  \text{Total surface area of cone = }\left( \pi rl + \pi r^2 \right) \text{sq. units} \\
  
  \end{aligned}

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• 5. Sphere Volume and Surface Area Formula

  
  

  Let the radius of the sphere be r, then,
  
  \begin{aligned}
  Volume = \left( \frac{4}{3}\pi r^3 \right) \text{cubic units} \\
  Surface Area = \left( 4\pi r^2 \right) \text{sq. units} \\
  \end{aligned}

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• 6. Hemisphere Volume, Curved Surface Area and Total Surface Area Formula

  
  

  Let the radius of a hemisphere be r, Then,
  \begin{aligned}
  \text{Volume of Hemisphere =} \left( \frac{2}{3} \pi r^3 \right) \text{cubic units} \\
  
  \text{Curved Surface area of Hemisphere =} \left( \frac{2}\pi r^2 \right) \text{sq. units} \\
  
  \text{Total Surface area of Hemisphere =} \left( 3 \pi r^2 \right) \text{sq. units} \\
  \text{Please remember 1 litre = }1000 cm^3
  \end{aligned}
  
  

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Volume and Surface Area Questions Answers