Question

The volume of a cylinder is 448 π cm³ and height 7 cm. Find its lateral (curved) surface area and total surface area
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Answer 1

Answer:

Step-by-step explanation:

Given :

Volume of the cylinder is 448π cm³,

height of the cylinder is 7 cm.

Let the radius be r cm.

We know that,

Volume of cylinder = πr²h

=> 448π = πr²h

=>  = r² × 7

=> 448 = r² × 7

=>  = r²

=> 64 = r²

=>  =r

=> 8 = r

Therefore,

the radius of the cylinder is 8 cm.

:

Lateral surface area and total surface area of the cylinder.

= 2πrh

= 2 ×  × 8 × 7

= 352 cm²

.

= 2πr(r + h)

= 2 ×  × 8 ( 8 + 7)

= 754.28 cm²

Answer 2

$\sf{volume \: of \: a \: cylinder = 448\pi \: {cm}^{3} }$

$\sf{height \: of \: cylinder = 7 \: cm}$

$\pink{ \boxed {\sf \purple{volume \: of \: cylinder = \pi {r}^{2} h}}}$

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

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: {r}^{2} = \frac{448\pi}{7\pi}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {r}^{2} = 64$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: r = 8 \: cm$

$\: \: \blue{ \boxed{\sf \red{csa \: of \: cylinder = 2\pi rh}}}$

$\: \: \: \: \: \: \: \: \: \: \: 2 \times \frac{22}{7} \times 8 \times 7$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 44 \times 8$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{352 \: {cm}^{2} }$

$\green{ \boxed{ \sf \pink{{tsa \: of \: cylinder = 2\pi r(r + h)}}}}$

$\: \: \: \: \: = > \: \: 2 \times \frac{22}{7} \times 8 (8 + 7)$

$\: \: \: \: \: = > \: \: \: \: \: \: 44 \times \frac{200}{7}$

$\: \: \: \: \: = > \: \: \: \: \: \sf{1257.14 {cm}^{2} }$