Question

the curved surface area of a right circular cylinder of height 14cm is 88cm^2. find the diameter of base of cylinder​

Answer 1

Given :

• Curved surface area = 88 cm²
• Height = 14 cm

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To Find :

• Diameter of base.

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Solution :

❒ Formula Used :

$\large{\color{aqua}{\bigstar}} \: \: \: {\underline{\boxed{\red{\sf{ C.S.A_{(Cylinder) } = 2πrh}}}}}$

$\qquad{▬▬▬▬▬▬▬▬▬▬▬▬▬▬}$

❒ Calculating the Radius :

${\leadsto{\qquad{\sf{ C.S.A = 2πrh}}}} \\ \\ \ {\leadsto{\qquad{\sf{ 88 = 2 \times \dfrac{22}{7} \times r \times 14 }}}} \\ \\ \ {\leadsto{\qquad{\sf{ 88 = 2 \times \dfrac{22}{\cancel7} \times r \times \cancel{14} }}}} \\ \\ \ {\leadsto{\qquad{\sf{ 88 = 2 \times 22 \times r \times 2}}}} \\ \\ \ {\leadsto{\qquad{\sf{ 88 = 44 \times r \times 2 }}}} \\ \\ \ {\leadsto{\qquad{\sf{ \cancel\dfrac{88}{44} = r \times 2}}}} \\ \\ \ {\leadsto{\qquad{\sf{ 2 = r \times 2}}}} \\ \\ \ {\leadsto{\qquad{\sf{ r = \cancel\dfrac{2}{2}}}}} \\ \\ \ {\qquad{\blue{\dashrightarrow{\orange{\underbrace{\underline{\rm{ Radius \: of \: Base \: = {\pink{\rm{1 \: cm }}}}}}}}}}}$

$\qquad{▬▬▬▬▬▬▬▬▬▬▬▬▬▬}$

❒ Calculating the Diameter :

${\leadsto{\qquad{\sf{ Diameter = 2 \times Radius }}}} \\ \\ \ {\leadsto{\qquad{\sf{ Diameter = 2 \times 1 }}}} \\ \\ \ {\qquad{\blue{\dashrightarrow{\orange{\underbrace{\underline{\rm{ Diameter \: of \: Base \: = {\pink{\rm{2 \: cm }}}}}}}}}}}$

$\qquad{▬▬▬▬▬▬▬▬▬▬▬▬▬▬}$

Therefore :

❝ Diameter of the Base is 2 cm. ❞

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