Question

A cylindrical vessel, open at the top,has a radius 10cm and height 14cm . Find the total surface area of the vessel. (take pai = 3.14)

Answer 1

Answer :1194.28 cm²

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Explanation:-

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• Given radius of the cylinderical vessel is 10 cm
• Height is 14 cm

So to find the total surface area or TSA of the cylinderical vessel whose top is open we can first find out the curved surface area or CSA of the Cylinderical vessel and then add the area of the circular base✓

Let ,us first find the CSA of the cylinderical vessel which is as follows

$= > CSA \: = 2\pi \: rh \\ \\ = > CSA \: = 2 \times \frac{22}{7} \times 10 \times 14 \\ (because \: \pi = \frac{22}{7} or \: in \: decimal \: form \: is \: 3.14) \\ \\ = > CSA \: = 2 \times 22 \times 10 \times 2 \\ \\ = > \: CSA \: = 44 \times 20 \\ \\ = >CSA \: = 880cm^{2}$

From the above calculation we find the CSA of the cylinderical vessel is 880 cm²✓

Now ,we need to find the area if the circular base which is as follows

$area \: of \: base = \pi \: r ^{2} \\ \\ = > area = \frac{22}{7} \times 10 ^{2} \\ \\ = > area = \frac{22}{7} \times 100 \\ \\ = > area = \frac{2200}{7} \\ \\ = >area = 314.28 \: cm ^{2}$

A/Q the total surface area or TSA of the cylinderical vessel whose top is open is the sum of CSA of the cylinderical vessel and area of circular base ✓

$= > TSA \: = (880 + 314.28)cm ^{2} \\ \\ = >TSA \: = 1194.28 \: cm ^{2}$

Therefore Total surface area of the cylinderical vessel is 1194.28 cm²