Question

find the height of a solid right circular cylinder who's total surface area is 2992cm² and the radius of cylinder is 14cm.

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Answer 1

Answer:

The height of a solid right circular cylinder who's total surface area is 2992cm² and the radius of the cylinder is 14cm is 20 cm.

Step-by-step explanation:

Given:

The total surface area of the right circular cylinder= 2992cm²

and the radius of cylinder = 14cm.

Find: Height

Formula: The total surface area of the right circular cylinder $=2\pi r(h + r)$

$2\times \frac{22}{7} \times 14 (h + 14)=2992\\2\times 22 \times 2 ( h + 14) = 2992\\88 ( h + 14) = 2992\\h + 14 =34\\h = 34 - 14\\h = 20 cm$

Hence the height of a solid right circular cylinder is 20 cm.

Answer 2

$\star \; {\underline{\boxed{\pmb{\orange{\sf{ \; Given \; :- }}}}}}$

• Total Surface Area = 2992 cm²
• Radius of Cylinder = 14 cm

$\star \; {\underline{\boxed{\pmb{\blue{\sf{ \; To \; Find \; :- }}}}}}$

• Height of Cylinder = ?

$\star \; {\underline{\boxed{\pmb{\pink{\sf{ \; SolutioN \; :- }}}}}}$

$\bigstar$ Formula Used :

• ${\underline{\boxed{\sf{ Total \; Surface \; Area = 2 \pi r \bigg( r + h \bigg) }}}}$

Where :

• ${\sf{ \pi = \dfrac{22}{7} }}$

• r = Radius
• h = Height

$\\ \qquad{\rule{150pt}{1pt}}$

$\bigstar$ Calculating the Height of Cylinder :

${\dashrightarrow{\qquad{\sf{ TSA = 2 \pi r \bigg( r + h \bigg) }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 2992 = 2 \times \dfrac{22}{7} \times 14 \bigg( 14 + h \bigg) }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 2992 = \dfrac{44}{7} \times 14 \bigg( 14 + h \bigg) }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 2992 = \dfrac{44}{\cancel7} \times \cancel{14} \bigg( 14 + h \bigg) }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 2992 = 44 \times 2 \bigg( 14 + h \bigg) }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 2992 = 88 \bigg( 14 + h \bigg) }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ \dfrac{2992}{88} = 14 + h }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ \cancel\dfrac{2992}{88} = 14 + h }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 34 - 14 = h }}}} \\ \\ \\ \ {\qquad \; \; {\therefore \; {\underline{\boxed{\pmb{\red{\frak{ Height = 20 \; cm }}}}}}}}$

$\\ \qquad{\rule{150pt}{1pt}}$

$\bigstar$ Therefore :

❛❛ Height of the given Cylinder is 20 cm . ❜❜

$\\ {\underline{\rule{300pt}{9pt}}}$