7 If the volume of a cylinder of height 7 cm. is 448 π cm, find its l

1.	7 If the volume of a cylinder of height 7 cm. is 448 π cm, find its lateral surface areaand total surface area.dan nala is 7 m highd 20cm in di
Answer» Dimensions of the cylinder : i ) Volume = v = 448/ pi cm^3------( 1 ) Height of the cylinder = 7 cm Let radius = r cm ____________________________ Volume of thecylinder = pi × r^2 × h----( 2 )_____________________________ 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

7 If the volume of a cylinder of height 7 cm. is 448 π cm, find its lateral surface areaand total surface area.dan nala is 7 m highd 20cm in di

Answer»

Dimensions of the cylinder :

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

Height of the cylinder = 7 cm

Let radius = r cm

____________________________

Volume of thecylinder = pi × r^2 × h----( 2 )_____________________________

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