In earlier classes, we have learnt how to find the surface area of the basic solids such as cube, cuboid, cone, cylinder, sphere and hemisphere.
Let us recall the formulas to find the surface area of the solids mentioned above.
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Solid
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Figure
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Total Surface Area (TSA) (in square units)
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Curved Surface Area (CSA) or Lateral Surface Area (LSA) (in square units)
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Formula description
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Cube
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\(6a^2\)
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\(4a^2\)
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\(a\) - side |
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Cuboid
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\(2(lb + bh +lh)\)
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\(2h(l + b)\)
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\(l\) - length
\(b\) - breadth
\(h\) - height
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Cone
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\(\pi r (l + r)\)
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\(\pi r l\)
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\(r\) - radius
\(l\) - slant height
\(l = \sqrt{r^2 + h^2}\)
\(h\) - height
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Cylinder
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\(2 \pi r (h + r)\)
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\(2 \pi r h\)
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\(r\) - radius
\(h\) - height
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Sphere
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\(4 \pi r^2\)
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\(4 \pi r^2\)
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\(r\) - radius |
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Hemisphere
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\(3 \pi r^2\)
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\(2 \pi r^2\)
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\(r\) - radius |
In our day-to-day life, we come across a wide range of objects that are in the form of a combination of two or more solid shapes.
Let us discuss some real-life examples in this article.
1.Circus tent
The circus tent is a combination of a cone and a cylinder.
2. Capsule
The capsule is a combination of two solids, cylinder and hemisphere.
Hence, to find the total surface area of the capsule is given by:
TSA of the capsule \(=\) CSA of the hemisphere \(+\) CSA of the cylinder \(+\) CSA of the hemisphere.
Example:
A capsule consists of a cylinder of height \(10\ cm\) with a hemisphere attached at each end. If the radius of the capsule is \(3.5\ cm\), find its total surface area.
Solution:
Total surface area of capsule \(=\) \(CSA\) of hemisphere \(+\) \(CSA\) of cylinder \(+\) \(CSA\) of second hemisphere
\(=2\pi r^2 + 2\pi r h + 2\pi r^2\)
\( = 4\pi r^2 + 2\pi r h\)
\(=2\pi r (2r + h)\) square units.
\(=2\times \frac{22}{7}\times 3.5(2(3.5)+10)\)
\(=374\ cm^2\)
Therefore, the area of the capsule is \(374\ cm^2\).
Important!
For combined solids, do not include the common surface where the two solids are joined. Only the exposed surfaces are counted.