Surface Area and Volume
Category : 9th Class
SURFACE AREA AND VOLUME
FUNDAMENTALS
Total surface Area of the cuboid \[=2\left( lb+bh+hl \right)\] sq. units.
Volume of the cuboid = \[l\times b\times h\]
Diagonal of the cuboid \[=\sqrt{{{l}^{2}}+{{b}^{2}}+{{h}^{2}}}\]
If length of each edge of a cube is a,
Then, volume of the cube \[={{a}^{3}}\]
Total surface area of the cube\[=6{{a}^{2}}\]
Diagonal of the cube \[=\sqrt{3a}.\]
Volume of the cylinder \[=\pi {{r}^{2}}h\]
Area of the base\[=\pi {{r}^{2}}\]
Area of the curved surface =\[2\pi rh\]
Total surface Area \[=2\pi rh+2\pi {{r}^{2}}h=2\pi r\left( h+r \right)\]
Radius = r. Height = h
Slant height = 1
Volume of the cone \[=\frac{1}{3}\pi {{r}^{2}}h\]
Area of the Base\[~=\pi {{r}^{2}}\]
Area of the curved surface \[=\pi r\sqrt{{{h}^{2}}+{{r}^{2}}}=\pi rl\]
OX = Radius = r
Volume of a sphere \[=\frac{4}{3}\pi {{r}^{3}}\]
Surface Area of a sphere \[=4\pi {{r}^{2}}\]
Radius = OX = r
Volume of a Hemisphere \[\frac{2}{3}\pi {{r}^{3}}\]
Curved surface area of a Hemisphere = \[2\pi {{r}^{2}}\]
Total surface area of a Hemisphere = \[3\pi {{r}^{2}}\]
Lateral surface area of a prism \[=perimeter\,of\,base\times Height\]
Whole surface = The slant surface + the area of the base
Volume of pyramid \[=\frac{1}{2}\left( perimeter\text{ }of\text{ }base \right)\times Slant\text{ }Height\]
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