Question

A solid cylinder has a total surface area of 462 sq.cm. Its curved surface area is one third of its total surface area. Find the volume of the cylinder.

Answer 1

Answer:

The Curved Surface Area is 154 cm².

Step-by-step explanation:

Given, Total Surface Area = 462 cm²

Curved Surface Area = 1/3 × 462 cm²

= 154 cm²

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Answer 2

GivEn:-

• Total Surface Area of Solid Cylinder = 462cm²

• It's Curved surface area is one third of its Total Surface Area.

To Find:-

• Volume of cylinder = ?

SoluTion:-

✠ DIAGRAM:

$\setlength{\unitlength}{1 mm}\begin{picture}(5,5)\qbezier(2,3)(8,8)(14,3)\qbezier(2,3)(8,-4)(14,3)\put(2,-27){\line(0,2){30}}\put(14,-27){\line(0,2){30}}\qbezier(2,-27)(8,-35)(14,-27)\qbezier(2,-27)(8,-20)(14,-27)\put(8,-27){\line(0,2){30}}\put(9,-14){ \tt{h} }\put(9,-29){ \tt{} }\put(8,-27){\line(2,0){6}}\put(8,3){\line(2,0){6}}\put(15,-14){ \tt{Total\:Surface\;Area = 462cm^{2}} }\put(9,-34){ \tt{} }\end{picture}$

$\dag\;\bf{\underline{\underline{\blue{According\;to\;question:-}}}}$

We have total Surface Area of cylinder,

$:\implies$ 2πr( r + h) 2πrh + 2πr²

$:\implies$ 2πrh + 2πr² = 462cm² --(1)

GivEn that,

★ Curved surface area = $\sf \dfrac{1}{3}$ × Total Surface Area

$:\implies$ 2πrh = $\sf \dfrac{1}{3}$ × 462 cm²

$:\implies$ 2πrh = 154 cm²

✠ Now, Substituting value of 2πrh in eq(1) -

$:\implies$ 154 cm² + 2πr² = 462 cm²

$:\implies$ 2πr² = 462 cm² - 154 cm²

$:\implies$ 2πr² = 308 cm²

$:\implies$ 2 × $\sf \dfrac{22}{7}$ × r² = 308 cm²

$:\implies$ r² = $\cancel{308}$ × $\sf \dfrac{7}{ \cancel{22}} \times \dfrac{1}{ \cancel{2}}$ cm²

✠ Taking sqrt both sides -

$:\implies\sf \sqrt{r^2} = \sqrt{49}$ cm²

$:\implies\sf {\underline{\red{r = 7\;cm}}}$

✠ Now, Substituting value of r in 2πrh -

$:\implies$ 2πrh = 154 cm²

$:\implies$ 2 × $\sf \dfrac{22}{ \cancel{7}} \times \cancel{7}$ × h= 154 cm²

$:\implies$ h = $\sf \cancel{154}$ × $\sf \dfrac{1}{ \cancel{44}}$

$:\implies\sf {\underline{\red{ h = \dfrac{7}{2} \;cm}}}$

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✠ Now, Finding Volume of Cylinder -

$\dag\;\bf {\underline{\boxed{\purple{Volume\;of\;cylinder = \pi r^2 h}}}}$

✠ Substituting Value of r and h -

$:\implies\sf \dfrac{ \cancel{22}}{ \cancel{7}} \times \cancel{7} \times 7 \times \dfrac{7}{ \cancel{2}}$

$:\implies\sf 11 \times 7 \times 7$

$:\implies\bf {\underline{\purple{539\;cm^3}}}$

$\dag$ Hence, Volume of cylinder is 539cm³.

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