Question

The volume of a cylinder is 448πcm³ and height 7cm. Find its lateral curved surface area and total surface area? (π=22/7)

Answer 1

AnswEr:

Let the radius of the base and height of the cylinder be r cm and h cm respectively. Then, h = 7 cm (given)

Now,

• Volume = 448 π cm³

$\Rightarrow$ $\tt{\pi\:r^2h\:448\pi}$

$\Rightarrow$ $\tt{\pi\:\times\:r^2\times\:7=448\pi}$

$= \tt {r}^{2} = \dfrac{448}{7} = 64 = r = 8 \: cm$

$\therefore$ $\tt\green{\underline{\underline{lateral\:surface\:area:-}}}$

$\tt = 2\pi \: rh \: {cm}^{2} \\ \\ \tt = 2 \times \frac{22}{7} \times 8 \times 7 \: {cm}^{2} = 352 \: {cm}^{2}$

$\therefore$ $\tt\purple{\underline{\underline{Total\:surface\:area:-}}}$

$\tt(2\pi \: rh + 2\pi \: r {}^{2}) \: {cm}^{2} \\ \\ \tt = 2\pi \: r(h + r) \: {cm}^{2}$

$\tt = 2 \times \dfrac{22}{7} \times 8(7 + 8) \: {cm}^{2} \\ \\ \tt = \frac{5280}{7 } \: {cm}^{2} \\ \\ \tt = 754.28 \: {cm}^{2}$

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Answer 2

Answer:

Step-by-step explanation: Let the radius of the base and height of the cylinder be r cm and h cm respectively. Then, h = 7 cm (given)

Now,

Volume = 448 π cm³

\Rightarrow \tt{\pi\:r^2h\:448\pi}

\Rightarrow \tt{\pi\:\times\:r^2\times\:7=448\pi}

=  \tt  {r}^{2}  =  \dfrac{448}{7}  = 64 = r = 8 \: cm

\therefore \tt\green{\underline{\underline{lateral\:surface\:area:-}}}

\tt = 2\pi \: rh \:  {cm}^{2}  \\  \\  \tt = 2 \times  \frac{22}{7} \times 8 \times 7  \: {cm}^{2}   = 352  \: {cm}^{2}  

\therefore \tt\purple{\underline{\underline{Total\:surface\:area:-}}}

\tt(2\pi \: rh + 2\pi \: r {}^{2})  \: {cm}^{2}   \\  \\  \tt = 2\pi \: r(h + r) \:  {cm}^{2}  

\tt = 2 \times  \dfrac{22}{7}  \times 8(7 + 8)  \: {cm}^{2}  \\  \\  \tt =  \frac{5280}{7 }  \:  {cm}^{2} \\  \\  \tt = 754.28 \:  {cm}^{2}  

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