Question

find the curved surface area , the total Surface area of right circular cylinder whose hight is 15cm and radius of base is 10.5cm​

Answer 1

Answer:

♦ The curved surface area of a circular cylinder = 990 cm²

♦ The total surface area of a circular cylinder = 1683 cm²

Step-by-step explanation:

Given:

• Height of a circular cylinder = 15 cm
• Radius of a base a circular cylinder = 10.5 cm

To find:

• The curved surface area of a circular cylinder.
• The total surface area of a circular cylinder.

Solution:

✰ Curved surface area = 2πrh

Where,

r is the radius of a circular cylinder.

h is the height of a circular cylinder.

Putting the values in the formula, we have:

• Curved surface area = 2 × 22/7 × 10.5 × 15
• Curved surface area = 44/7 × 10.5 × 15
• Curved surface area = 44/7 × 157.5
• Curved surface area = 6930/7
• Curved surface area = 990 cm²

✰ Total surface area = 2πr ( h + r )

Where,

r is the radius of a circular cylinder.

h is the height of a circular cylinder.

Putting the values in the formula, we have:

• Total surface area = 2 × 22/7 × 10.5 ( 15 + 10.5 )
• Total surface area = 2 × 22/7 × 10.5 × 25.5
• Total surface area = 44/7 × 10.5 × 25.5
• Total surface area = 44/7 × 267.75
• Total surface area = 11781/7
• Total surface area = 1683 cm²

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Answer 2

Given that , The Height of Cylinder is 15 cm & Radius of base of Cylinder is 10.5 cm .

Need To Find : The Total Surface Area [ T.S.A ] & Curved surface area [ C.S.A ] of Cylinder .

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⠀⠀⠀⠀⠀⠀⠀⠀¤ Finding Total Surface Area ( T.S.A ) of Cylinder :

As , We know that ,

⠀⠀⠀➠ TOTAL SURFACE AREA of Cylinder :

$\qquad \star \:\:\underline {\boxed {\bf {\pink { \:\: T.S.A _{(\:Cylinder \:)}\:\:=\:\: 2\pi r \bigg( h + r \bigg)\:\:sq.units \:\:}}}}$

⠀⠀⠀⠀⠀Here , r is the Base Radius of Cylinder , h is the Height of the cylinder & $\sf \pi \:=\:\dfrac{22}{7}$.

$\qquad \dashrightarrow \sf \:\: T.S.A _{(\:Cylinder \:)}\:\:=\:\: 2\pi r \bigg( h + r \bigg)\:$

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\qquad \dashrightarrow \sf \:\: T.S.A _{(\:Cylinder \:)}\:\:=\:\: 2\pi r \bigg( h + r \bigg)\:$

$\qquad \dashrightarrow \sf \:\: T.S.A _{(\:Cylinder \:)}\:\:=\:\: 2 \times \dfrac{22}{7} \times 10.5 \bigg( 15 + 10.5 \bigg)\:$

$\qquad \dashrightarrow \sf \:\: T.S.A _{(\:Cylinder \:)}\:\:=\:\: 2 \times \dfrac{22}{7} \times 10.5 \bigg( 25.5 \bigg)\:$

$\qquad \dashrightarrow \sf \:\: T.S.A _{(\:Cylinder \:)}\:\:=\:\: \dfrac{44}{7} \times 10.5 \bigg( 25.5 \bigg)\:$

$\qquad \dashrightarrow \sf \:\: T.S.A _{(\:Cylinder \:)}\:\:=\:\: \dfrac{44}{7} \times 267.75\:$

$\qquad \dashrightarrow \sf \:\: T.S.A _{(\:Cylinder \:)}\:\:=\:\: \dfrac{44}{\cancel {7}} \times \cancel {267.75}\:$

$\qquad \dashrightarrow \sf \:\: T.S.A _{(\:Cylinder \:)}\:\:=\:\: 44 \times 38.25\:$

$\qquad \dashrightarrow \sf \:\: T.S.A _{(\:Cylinder \:)}\:\:=\:\: 1683 \:\:$

$\qquad \therefore \:\: \underline{\boxed{\purple {\pmb {\frak{ \:\: T.S.A _{(\:Cylinder \:)}\:\:=\:\: 1683\:cm^2 \:\:}}}}}$

$\qquad \therefore \:\:\underline {\sf Hence,\:The\:Total \:Surface \:Area\:of \:Cylinder \:is \: \bf 1683\;cm^2 \:\:}$

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⠀⠀⠀⠀⠀⠀⠀⠀¤ Finding Curved Surface Area ( C.S.A ) of Cylinder :

As , We know that ,

⠀⠀⠀➠ CURVED SURFACE AREA of Cylinder :

$\qquad \star \:\:\underline {\boxed {\bf {\pink { \:\: C.S.A _{(\:Cylinder \:)}\:\:=\:\: 2\pi r h\:\:sq.units \:\:}}}}$

⠀⠀⠀⠀⠀Here , r is the Base Radius of Cylinder , h is the Height of the cylinder & $\sf \pi \:=\:\dfrac{22}{7}$.

$\qquad \dashrightarrow \sf \:\: C.S.A _{(\:Cylinder \:)}\:\:=\:\: 2\pi r h\:$

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\qquad \dashrightarrow \sf \:\: C.S.A _{(\:Cylinder \:)}\:\:=\:\: 2\pi r h\:$

$\qquad \dashrightarrow \sf \:\: C.S.A _{(\:Cylinder \:)}\:\:=\:\: 2\times \dfrac{22}{7}\times 10.5 \times 15\:$

$\qquad \dashrightarrow \sf \:\: C.S.A _{(\:Cylinder \:)}\:\:=\:\: \dfrac{44}{7}\times 10.5 \times 15\:$

$\qquad \dashrightarrow \sf \:\: C.S.A _{(\:Cylinder \:)}\:\:=\:\: \dfrac{44}{7}\times 157.5\:$

$\qquad \dashrightarrow \sf \:\: C.S.A _{(\:Cylinder \:)}\:\:=\:\: \dfrac{44}{\cancel {7}}\times \cancel{157.5}\:$

$\qquad \dashrightarrow \sf \:\: C.S.A _{(\:Cylinder \:)}\:\:=\:\: 44\times 22.5\:$

$\qquad \dashrightarrow \sf \:\: C.S.A _{(\:Cylinder \:)}\:\:=\:\: 990\:$

$\qquad \therefore \:\: \underline{\boxed{\purple {\pmb {\frak{ \:\: C.S.A _{(\:Cylinder \:)}\:\:=\:\: 990\:cm^2 \:\:}}}}}$

$\qquad \therefore \:\:\underline {\sf Hence,\:The\:Curved \:Surface \:Area\:of \:Cylinder \:is \: \bf 990\;cm^2 \:\:}$

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