Question

the volume of a cylinder is 448 pie cm cube abd its height is 7cm. Find the curved surface area and total surface area of a cylinder

Answer 1

Volume of Cylinder
$= \pi {r}^{2}h$
$= > \pi {r}^{2}h = 448\pi \\ = > {r}^{2}7 = 448 \\ = > {r}^{2} = \frac{448}{7} = 64 \\ = > r = 8cm.$



C. S. A of Cylinder
$= 2\pi \: rh \\ = 2 \times \frac{22}{7} \times 8 \times 7 \\ = 352 {cm}^{2}.$


T. S. A of Cylinder
$= 2\pi \: r(r + h) \\ = 2 \times \frac{22}{7} \times 8(8 + 7) \\ = \frac{2 \times 22 \times 8 \times 15}{7} \\ = 754.29 {cm}^{2}.$




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Answer 2

As we know that,

=> Volume of Cylinder = πr^2h

=> 448 π = πr^2 x 7 cm

=> r^2 x 7 = 448

=> r^2 = 448/7

=> r^2 = 64

$= > r \: \: = \sqrt{64} = 8 \: cm$

Now,

C.S.A of Cylinder = 2πrh

=> CSA = 2 x 22/7 x 8 x 7

=> C.S.A = (2 x 22 x 8) cm^2

=> C.S.A = 352 cm^2


Again,

TSA of Cylinder = 2πr(r+h)

=> TSA = 2 x 22/7 x 8(8+7)

=> TSA = 2 x 22/7 x 8 x 15

=> T.S.A = 754.28 cm^2



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