Surface area and volume (Solid shapes)
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Surface area and volume (Solid shapes) Chapter 13 Class X
Interactive 3d shape, formulas volume and surface area, surface area and volume formulas class 9th and 10th , 3d shape formulas volume and surface area for class 9th,
These are also be called solid shapes because all these figures are involve three dimensions.
Further these are classified into different types. Main types are cube, cuboid, cylinder, cone, sphere, hemi-sphere and frustum of cone.
Here in this topic we discussed surface area and volume of these shapes.
CUBE \[Curved Surface
Area=4(side)^{2}\] \[Total Surface
Area=6(side)^{2}\] \[Volume =
(Side)^{3}\] |
CUBOID \[Curved Surface
Area = 2(l+b)\times h\] \[Total Surface Area
= 2(lb+bh+hl)\] Volume = Length X Breadth X Height |
CYLINDER \[Curved Surface
Area = 2\pi rh\] \[Total Surface Area
= 2\pi r\left ( r+h \right )\] \[Volume=\pi
r^{2}h\] |
CONE \[Curved\: Surface\:
Area\\=\pi rl\: \: where\:\: l=\sqrt{h^{2}+r^{2}}\] \[Total\; Surface\;
Area=\pi r\left ( r+l \right )\] \[Volume\; =\;
\frac{1}{3}\pi r^{2}h\] |
SPHERE \[Curved\; Surface\;
Area=\: 4\pi r^{2}\] \[Total\; Surface\;
Area=\: 4\pi r^{2}\] \[Volume=\:
\frac{4}{3}\pi r^{3}\] |
HEMI-SPHERE \[Curved\; Surface\;
Area=2\pi r^{2}\] \[Total\; Surface\;
Area=3\pi r^{2}\] \[Volume=\frac{2}{3}\pi
r^{3}\] |
HOLLOW CYLINDRICAL PIPE \[Inner\; Curved\;
Surface\; Area=2\pi rh\] \[Outer\; Curved\;
Surface\; Area=2\pi Rh\] \[Area\; of\; Two\;
Rims=2\pi \left ( R^{2}-r^{2} \right )\] \[Total\; Surface\;
Area\\=\pi R^{2}h+\pi r^{2}h+2\pi \left ( R^{2}-r^{2} \right )\] \[Volume=\pi h\left
( R^{2}-r^{2} \right )\] |
FRUSTUM OF CONE \[Curved\; Surface\;
Area=\pi l\left ( r_{1}+r_{2} \right ) \\ where\, \, l=\sqrt{h^{2}+\left (
r_{1}-r_{2}\right )^{2}}\] \[Total\; Surface\;
Area\\=\pi l\left ( r_{1}+r_{2} \right )+\pi r_{1}^{2}+\pi r_{2}^{2} \\ \, \,
l=\sqrt{h^{2}+\left ( r_{1}-r_{2}\right )^{2}}\] \[Volume=\frac{1}{3}\pi
h\left [ r_{1}^{2}+r_{2}^{2}+r_{1}r_{2} \right ]\] |
Solid Figure |
Curved Surface Area |
Total Surface Area |
Volume |
CUBE |
\[4\times \left ( side \right )^{2}\] |
\[6\times \left ( side \right )^{2}\] |
\[\left ( side \right )^{3}\] |
CUBOID |
\[2\left ( l+b \right )\times h\] |
\[2\left ( lb+bh+hl \right )\] |
\[lbh\] |
CYLINDE |
\[2\pi rh\] |
\[2\pi rh+\pi r^{2}+\pi r^{2}\]\[=2\pi r\left ( r+h \right )\] |
\[\pi r^{2}h\] |
CONE |
\[\pi rl\] |
\[\pi r\left ( r+l \right )\] |
\[\frac{1}{3}\pi r^{2}h\] |
SPHERE |
\[4\pi r^{2}\] |
\[4\pi r^{2}\] |
\[\frac{4}{3}\pi r^{3}\] |
HEMI - SPHERE |
\[2\pi r^{2}\] |
\[3\pi r^{2}\] |
\[\frac{2}{3}\pi r^{3}\] |
FRUSTUM OF CONE |
\[\pi l\left ( r_{1}+r_{2} \right )\] |
\[\pi l\left ( r_{1}+r_{2} \right )+\pi r_{1}^{2}+\pi r_{2}^{2}\] |
\[\frac{1}{3}\pi h\left [ r_{1}^{2}+r_{2}^{2}+r_{1}r_{2} \right ]\] |
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