Question

The volume of a right circular cylinder of height 12 cm is 29568cm cube. Find its curved surface area(π =22/7)

Answer 1

Step-by-step explanation:

Volume of right circular cylinder :

$\implies$ $\sf{V=πr^2h }$

$\implies$ $\sf{29568={\Large\frac{22}{7}}×12×r^2 }$

$\implies$ $\sf{r^2= {\Large\frac{29568×7}{22×12}}}$

$\implies$ $\sf{r=\sqrt{784} }$

$\implies$ $\sf{r=28cm }$

Curved surface area :

$\implies$ $\sf{CSA=2πrh }$

$\implies$ $\sf{2×{\Large\frac{22}{7}}×28×12 }$

$\implies$ $\sf{2×22×4×12 }$

$\implies$ $\boxed{\sf{CSA=2112cm^2} }$

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Answer 2

Volume of a right circular cylinder =

$\pi {r}^{2}h$

$</p><p>=> 29568 = 22/ \div 7 \times {r}^{2} \times 12 \\ </p><p>=> 29568 \div 12 = 22 \div 7 \times {r}^{2} \\ </p><p>=> 2464 = 22 \div 7 \times {r}^{2} \\ </p><p>=> 2464 \div 22 = 1 \div 7 \times {r}^{2} \\ </p><p>=> 112 = 1 \div 7 \times {r}^{2} \\ </p><p>=> 112 \times 7 = {r}^{2} \\ </p><p>=> 784 = {r}^{2} \\ </p><p>=> r = \sqrt{784} \\ </p><p> = > r \: = \sqrt{28 \times 28} \\ = > r \: = 28 \: cm$

Now ,

Curved surface area of a cylinder =

$2\pi \ rh$

$= > 2 \times 22 \div 7 \times 28 \times 12 \\ = > 2\times 22 \times 4 \times 12 \\ = > 22 \times 24 \\ = > 2112 \: c {m}^{2} (answer)$