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### Formulas for Problems on Volume and Surface Area - Aptitude Questions and Answers.

TIPS FOR SOLVING QUESTIONS RELATED TO VOLUME AND SURFACE AREA:

 1. Cube Let edge of a cube = 'a' unit, then \begin{aligned} \text{Volume of cube =} \left( a^3 \right) \text{cub. units}\\ \text{Surface Area of cube =} \left( 6a^2 \right) \text{sq. units} \\ \text{Diagonal of cube =} \left( \sqrt{3}a \right) \text{units}\\ \end{aligned}

2. Cuboid
Let length = l unit, breadth = b unit and height = h unit. 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}

3. Sphere
Let radius of the sphere = r unit, 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}

4. Hemisphere
Let radius of the sphere = r unit, 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} \\
\end{aligned}

5. Cone
Let radius of the base = r unit and height of the cone = h unit. 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}

6. Cylinder
Let radius of the base = r unit and height of the cylinder = h unit. Then, \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}