Question

Q.11. Find the area of base and radius of cylinde, if its curved surface area is 660 sq.cm. and height
s 21 cm. (pie 3.14)
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Answer 1

$\sf\small\underline\green{Given:-}$

$\tt{\implies C.S.A\:_{(Cylinder)}=660cm^2}$

$\tt{\implies Height\:_{(Cylinder)}=21cm}$

$\sf\small\underline\green{To\: Find:-}$

$\tt{\implies Area\:_{(base\:of\:cylinder)}=?}$

$\sf\small\underline\green{Formula\:used:-}$

$\tt{\implies C.S.A\:_{(Cylinder)}=2\pi\:r\:h}$

$\sf\small\underline\green{Solution:-}$

To calculate the area of base of cyclinder ,at first we have to find the radius of cyclinder with the help of applying formula of CSA of cyclinder. Then calculate it's base area with the help of formula.

$\tt{\implies C.S.A\:_{(Cylinder)}=660}$

$\tt{\implies 2*3.14*r*21=660}$

$\tt{\implies 131.88r=660}$

$\tt{\implies r=5.0cm}$

$\tt{\implies Area\:_{(base\:of\:cylinder)}=\pi\:r^2}$

$\tt{\implies Area\:_{(base\:of\:cylinder)}=3.14*5.0*5.0}$

$\tt{\implies Area\:_{(base\:of\:cylinder)}=78.5cm^2}$

$\sf\large{Hence,}$

$\tt{\implies Area\:_{(base\:of\:cylinder)}=78.5cm^2}$

Answer 2

Given

• ➠ The curved surface area of cylinder is 660 sq.cm.
• ➠ The height of cylinder is 21 cm.

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To Find

• ➠ Find the area of base and radius of cylinde.

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Solution

Finding Radius of cylinder by using "Curved surface area of cylinde" Formula..

As we know that

${ \underline{ \boxed{ \sf{Curved \: surface \: area \: of \: cylinder = 2{\pi}rh}}}}$

• Substituting the values

$: \implies \sf \pink{660}= \purple {2 \times \dfrac{22}{7} \times r \times21 }$

$: \implies \sf \pink{660}= \purple {2 \times \dfrac{22} {\cancel{7}} \times r \times \cancel{21 }}$

$: \implies \sf \pink{660}= \purple {2 \times {22}\times r \times3 }$

$: \implies \sf \pink{660}= \purple {2 \times {22}\times r \times3 }$

$: \implies \sf \pink{660}= \purple { {132}\times r }$

$: \implies \sf \pink {\cancel{\dfrac{660}{132} }}= \purple{r}$

$\: \: \large \underline{\boxed {\pmb {\frak \purple{r }= \frak\pink {5 \: cm}}}}$

• ➥The radius of cylinder is 5 cm

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Now Finding the Height of Cylinder by applying "Area of a base of the cylinder" formula.

As we know that.

$\underline{\boxed{ \sf{Area \: of \: a \: base \: of \: the \: cylinde}r = {{ \pi}r2}}}$

• Substituting the values

$: \implies \sf \purple{Cylinder \: Base_{(Area)} = \pink{ \dfrac{22}{7} \times {5}^{2}}}$

${ : \implies \sf \purple{Cylinder \: Base_{(Area)} = \pink{ \dfrac{22}{7} \times {5 \times 5}}}}$

$: \implies \sf \purple{Cylinder \: Base_{(Area)} = \pink {\cancel{ \dfrac{550}{7}}}}$

${: \implies \sf \purple{Cylinder \: Base_{(Area)} = \pink{ 78.57 \: {cm}^{2} }}}$

$\large \underline {\boxed{ \pink{ \frak {\pmb{{Cylinder \: Base_{(Area)} = \purple{ 78.57 \: {cm}^{2} }}}}}}}$

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Therefore

• ➥The radius of the cylinder is 5 cm and the area of its base is 78.57cm²