Question

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

Answer 1

Given :

• Radius of cylindrical vessel, r = 10 cm
• Height of cylindrical vessel, h = 14 cm

To find :

• Total surface area of vessel?

Solution :

Given,

• Cylindrical vessel is open at top.

So,

Total surface area of vessel is,

→ Curved surface area of vessel + Area of base

→ 2πrh + πr²

→ 2 × 3.14 × 10 × 14 + 3.14 × (10)²

→ 2 × 3.14 × 10 × 14 + 3.14 × 100

→ 879.2 + 314

→ 1193.2 cm²

Hence, Total surface area of the cylindrical vessel is 1193.2 cm².

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More to know:

• Curved surface area of cylinder = 2πrh
• Total surface area of cylinder = (2πrh + 2πr²) = 2πr(r + h)
• Volume of cylinder = πr²h

Answer 2

$\huge{ \underline{ \rm{ \large{ \pink{Given:}}}}}$

• Radius of cylinder vessel = 10cm
• Height of cylinder vessel = 14cm

$\huge { \underline{ \large{ \rm{ \red{Find:}}}}}$

• Total surface area of vessel

$\huge{ \underline{ \large{ \rm{ \green{Solution:}}}}}$

We know that, ⤵

TSA of vessel = CSA of vessel + area of base

$\: \: \: \: \: \: \: { \large{ \boxed{ \sf{TSA = 2\pi \: rh + \pi \: {r}^{2} }}}}$

${ \implies{2 \times \frac{22}{7} \times 10 \times 14 + \frac{22}{7} \times {10}^{2} }}$

${ \implies{2 \times 22 \times 10 \times 2 + \frac{22}{7} \times 100 }}$

${ \implies{880 + \frac{2200}{7} }}$

${ \implies{ \frac{6160 + 2200}{7} }}$

${ \implies{ \frac{8360}{7} }}$

${ \implies{1194.2c {m}^{2} }}$

${ \therefore{ \sf{ \blue{TSA \: of \: the \: v essel \: is \: 1194.2 cm²}}}}$