Question

the volume of a right circular cylinder is 448 pi cubic cm and height is 7 cm . Find it's lateral surface area and total surface area

Answer 1

Here is the answer
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Answer 2

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

=> $\frac{448\pi}{\pi}$ = r² × 7

=> 448 = r² × 7

=> $\frac{448}{7}$ = r²

=> 64 = r²

=> $\sqrt{64}$ =r

=> 8 = r

Therefore,
the radius of the cylinder is 8 cm.

$\mathbb{TO\:BE\:FOUND}$ :
Lateral surface area and total surface area of the cylinder.

$\bf{Lateral\:surface\: area \: :}$
= 2πrh

= 2 × $\frac{22}{7}$ × 8 × 7

= 352 cm²

.

$\bf{Total\:surface\: area \: :}$
= 2πr(r + h)

= 2 × $\frac{22}{7}$ × 8 ( 8 + 7)

= 754.28 cm²