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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{(a) Volume of Cube} \\
= \left( a^3 \right) \text{cub. units}\\
\\
\text{(b) Surface Area of Cube} \\
= \left( 6a^2 \right) \text{sq. units} \\
\\
\text{(c) 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{(a) Volume of Cuboid} \\
=(l*b*h)\text{cubic units} \\
\\
\text{(b) Surface Area of Cuboid} \\
= 2(lb + bh +hl)\text{sq. units}\\
\\
\text{(c) Diagonal of Cuboid} \\
= \sqrt{l^2+b^2+h^2} units
\end{aligned}
3. Sphere
Let radius of the sphere = r unit, then
\begin{aligned}
\text{(a) Volume of Sphere} \\
= \left( \frac{4}{3}\pi r^3 \right) \text{cubic units} \\
\\
\text{(b) Surface Area of Sphere} \\
= \left( 4\pi r^2 \right) \text{sq. units}
\end{aligned}
4. Hemisphere
Let radius of the sphere = r unit, then
\begin{aligned}
\text{(a) Volume of Hemisphere} \\
= \left( \frac{2}{3} \pi r^3 \right) \text{cubic units} \\
\\
\text{(b) Curved Surface Area of Hemisphere} \\
= \left( \frac{2}\pi r^2 \right) \text{sq. units} \\
\\
\text{(c) 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{(a) Slant Height of Cone, l} \\
= \sqrt{r^2+h^2} units \\
\\
\text{(b) Volume of Cone} \\
= \left( \frac{1}{3}\pi r^2 h \right) \text{cubic units} \\
\\
\text{(c) 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{(a) Volume of Cylinder} \\
= (\pi r^2 h)\text{cubic units} \\
\\
\text{(b) Curved Surface Area of Cylinder} \\
= (2\pi r h) \text{sq. units}\\
\\
\text{(c) 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}