Question

the volume of a cylinder is 448 /pi cm cube and height 7 cm. find its lateral surface area and total surface area.

Answer 1

Hi ,

Dimensions of the cylinder :

i ) Volume = v = 448/ pi cm^3------( 1 )

Height of the cylinder = 7 cm

Let radius = r cm

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Volume of the
cylinder = pi × r^2 × h----( 2 )
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Put the values in ( 2 )

pi × r^2 × h = 448 / pi

pi × r^2 × 7 = 448/ pi

r^2 = ( 448 ) / ( pi × pi × 7 )

r^2 = 64 / ( pi × pi )

Therefore ,

r^2 = ( 8 / pi )^2

r = 8/ pi cm

ii ) Lateral Surface Area ( LSA )

= 2 × pi × r × h

= 2 × pi × 8/ pi × 7

= 2 × 8 × 7

= 112 cm^2

iii) Total surface area ( TSA )

= 2 × pi × r ( r + h )

= 2 × pi × 8/ pi ( 8/ pi + 7 )

= 2 × 8 [ ( 8 × 7)/ 22 + 7 ]

= 16 ( 28 / 11 + 7 )

= 16 ( 28 + 77 )/ 11

= ( 16 × 105 )/ 11

= 1680/11

= 152. 72 cm^2

I hope this helps you.

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