Question

Find the curved surface area and total surface area of a right circular cylinder whose height is 15 cm and the radius of the base is 7 cm
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Answer 1

AnswEr-:

$\sf{\bf{Given-:}}$

• The Height of Right Circular Cylinder is 15 cm .

• The Base Radius of Right Circular Cylinder is 7 cm .

$\sf{\bf{To\:Given-:}}$

• Curved Surface Area and Total Surface Area of Cylinder.

$\mathrm {\bf{\dag{Solution \:of\:Question-:}}}$

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$\mathrm {\bf{\star{Finding\:Curved\:Surface\:Area\:of\:Cylinder\:-:}}}$

• $\underline{\boxed{\star{\sf{\red{  Curved\:Surface\:Area\:of\:Cylinder \:=\:2 \times \pi \times Radius \times Height \: sq.units }}}}}$

$\sf{\bf{Here-:}}$

• The Height of Right Circular Cylinder is 15 cm .

• The Base Radius of Right Circular Cylinder is 7 cm .

• $\pi$ = $\dfrac{22}{7}$

Now by putting known Values in Formula for Curved surface area of Cylinder-:

• $\qquad \quad \qquad \quad \longmapsto{\mathrm { C.S.A \:= 2 \times \dfrac{22}{7} \times 7 \times 15 }}$

• $\qquad \quad \qquad \quad \longmapsto{\mathrm { C.S.A \:= 2 \times \dfrac{22}{\cancel {7}} \times \cancel {7} \times 15 }}$

• $\qquad \quad \qquad \quad \longmapsto{\mathrm { C.S.A \:= 2 \times 22 \times 15 }}$

• $\qquad \quad \qquad \quad \longmapsto{\mathrm { C.S.A \:= 44 \times 15 }}$

• $\qquad \quad \qquad \quad \underline {\boxed{\pink{\mathrm { C.S.A \:= 660cm^{2} }}}}$

Therefore,

• $\underline {\star{\pink{\mathrm { C.S.A \:or\: Curved \:Surface \:Area\:of\:Cylinder \:= \: 660cm^{2} }}}}$

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$\mathrm {\bf{\star{Finding\:Total\:Surface\:Area\:of\:Cylinder\:-:}}}$

• $\underline{\boxed{\star{\sf{\red{ Total \:Surface\:Area\:of\:Cylinder \:=\:2 \times \pi \times Radius ( Height+ Radius) \: sq.units }}}}}$

$\sf{\bf{Here-:}}$

• The Height of Right Circular Cylinder is 15 cm .

• The Base Radius of Right Circular Cylinder is 7 cm .

• $\pi$ = $\dfrac{22}{7}$

Now by putting known Values in Formula for Total surface area of Cylinder-:

• $\qquad \quad \qquad \quad \longmapsto{\mathrm { T.S.A \:= 2 \times \dfrac{22}{7} \times 7 ( 15+7) }}$

• $\qquad \quad \qquad \quad \longmapsto{\mathrm { T.S.A \:= 2 \times \dfrac{22}{\cancel {7}} \times \cancel {7} ( 15+7) }}$

• $\qquad \quad \qquad \quad \longmapsto{\mathrm { T.S.A \:= 2 \times 22 \times ( 15+7) }}$

• $\qquad \quad \qquad \quad \longmapsto{\mathrm { T.S.A \:= 2 \times 22 \times 22 }}$

• $\qquad \quad \qquad \quad \longmapsto{\mathrm { T.S.A \:= 44 \times 22 }}$

• $\qquad \quad \qquad \quad \underline {\boxed{\pink{\mathrm { T.S.A \:= 968cm^{2} }}}}$

Therefore,

• $\underline {\star{\pink{\mathrm { T.S.A \:or\: Total \:Surface \:Area\:of\:Cylinder \:= \: 968cm^{2} }}}}$

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Hence ,

• $\underline {\star{\pink{\mathrm { C.S.A \:or\: Curved \:Surface \:Area\:of\:Cylinder \:= \: 660cm^{2} }}}}$

• $\underline {\star{\pink{\mathrm { T.S.A \:or\: Total \:Surface \:Area\:of\:Cylinder \:= \: 968cm^{2} }}}}$

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Answer 2

$\Huge{\mathfrak{\purple{\underline{\pink{Solution}}}}}$

Given:-

• Height of C.S.A and T.S.A. is 15cm.
• Radius is 7cm.

To Find:-

• To find C.S.A nad T S.A = ?

Solution:-

Let's understand

Here,Height of C.S.A and T.S.A is given 15cm and it's radius is 7cm and we have to find C.S.A and T.S.A.

We know that,

$\large\sf\red{Curved\:Surface\:Area\:of\:Cylinder=2×π×Radius×Height\:sq.\:units}$

Now,Put the value

$\sf \implies \: c.s.a = 2 \times \frac{22}{7} \times 7 \times 15 \\ \\ \sf \implies \: c.s.a = 2 \times 22 \times 15 \\ \\ \sf \implies \: c.s.a = 44 \times 15 \\ \\ \sf \implies \: c.s.a = 660 {cm}^{2}$

Hence, Curved Surface Area is 660$\sf{cm}^{2}$.

After finding C.S.A now we have to find T.S.A.

We know that,

$\large\sf\blue{Total\:Surface\:Area\:of\:Cylinder=2×π×Radius(Height + Radius)sq.\:units}$

Now put the values

$\sf \implies \: t.s.a = 2 \times \frac{22}{7} \times 7(15 + 7) \\ \\ \sf \implies \: t.s.a = 2 \times 22 \times (15 + 7) \\ \\ \sf \implies \: t.s.a = 2 \times 22 \times 22 \\ \\ \sf \implies \: t.s.a = 44 \times 22 \\ \\ \sf \implies \: t.s.a = 968 {cm}^{2}$

Hence, Total Surface Area is 968$\sf{cm}^{2}$.