Question

The circumference of the base of a cylinder is 88cm and its height is 65cm.
Find its total surface area.

Answer 1

1. Using the circumference you can find radius.
2. Then put the radius with the height given on the formula of circle total surface area 2π(h+r)

Answer 2

Given :

• Circumference of Base = 88 cm
• Height of Cylinder = 65 cm

To Find :

• Total Surface Area = ?

Solution :

$\pink\clubs$ Formula Used :

• ${\underline{\boxed{\red{\sf{ Circumference{\small_{(Circle)}} = 2 \pi r }}}}}$

• ${\underline{\boxed{\red{\sf{ TSA{\small_{(Cylinder)}} = 2 \pi r \bigg( h + r \bigg) }}}}}$

Where :

• ➬ ${\sf{ \pi = \dfrac{22}{7} }}$

• ➬ r = Radius
• ➬ h = Height

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$\pink\clubs$ Calculating the Radius :

${\longmapsto{\qquad{\sf{ Circumference = 2 \pi r }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 88 = 2 \times \dfrac{22}{7} \times r }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 88 = 2 \times \dfrac{22}{7} \times r }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 88 = \dfrac{44}{7} \times r }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 88 \times 7 = 44 \times r }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ 616 = 44 \times r }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ \dfrac{616}{44} = r }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ \cancel\dfrac{616}{44} = r }}}} \\ \\ \\ \ {\qquad \; \; {\therefore \; {\underline{\boxed{\color{darkblue}{\pmb{\frak{ Radius = 14 \; cm }}}}}}}}$

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$\pink\clubs$ Calculating the TSA :

${\dashrightarrow{\qquad{\sf{ TSA = 2 \pi r \bigg( h + r \bigg) }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ TSA = 2 \times \dfrac{22}{7} \times 14 \bigg(65 + 14 \bigg) }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ TSA = 2 \times \dfrac{22}{\cancel7} \times \cancel14 \bigg(65 + 14 \bigg) }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ TSA = 2 \times 22 \times 2 \bigg(65 + 14 \bigg) }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ TSA = 2 \times 22 \times 2 \times 79 }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ TSA = 44 \times 2 \times 79 }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ TSA = 88 \times 79 }}}} \\ \\ \\ \ {\qquad \; \; {\therefore \; {\underline{\boxed{\color{orange}{\pmb{\frak{ Total \; Surface \; Area = 6952 \; {cm}^{2} }}}}}}}}$

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$\pink\clubs$ Therefore :

❛❛ Total Surface Area of the given Cylinder is 6952 cm² . ❜❜

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