Question

the volume of a cylinder is 2500 pie cm3 and its height is 49cm . find the total surface area and lateral surface area of the cylinder ​

Answer 1

Step-by-step explanation:

Total surface area of cylinder = 2519.69 cm²

Lateral surface area of cylinder = 2200 cm²

Step-by-step explanation:

The volume of a cylinder is 2500π cm³

Height of cylinder, h = 49 cm

\pi r^2h=2500\piπr

2

h=2500π

\pi \times r^2\times 49=2500\piπ×r

2

×49=2500π

r=\dfrac{50}{7}r=

7

50

Total surface area of cylinder, T=2\pi rh+2\pi r^2T=2πrh+2πr

2

T=2\pi\times\dfrac{50}{7}\times 49 +2\pi \times (\dfrac{50}{7})^2T=2π×

7

50

×49+2π×(

7

50

)

2

T=2519.69\ cm^2T=2519.69 cm

2

Lateral surface area of cylinder, L=2\pi rhL=2πrh

L=2\pi\times \dfrac{50}{7}\times 49L=2π×

7

50

×49

L=2200\ cm^2L=2200 cm

2

Answer 2

Step-by-step explanation:

$\huge\sf\underline\purple{answer}$

given,

volume of cylinder = 2500πcm³

height of cylinder = 49cm

.: Volume of the cylinder = πr²h

2500πcm³ = π×r²×49cm

2500cm³ = r²×49cm

r² = 2500cm³/49cm

r² = 2500cm²/49

r² = (50cm/7)²

.: r = 50/7cm

TOTAL SURFACE AREA OF CYLINDER:

.: T.S.A = 2πr(r+h)

= 2×π×50/7(50/7+49)

= 2×π×50/7((393/7)

=100/7×π×393/7

= 39300/49×π

= 802.04πcm²

CURVED SURFACE AREA OF CYLINDER:

.: C.S.A = 2πrh

= 2×π×50/7×49

= 100×7×π

= 700πcm²

.: T.S.A = 802.04πcm², C.S.A = 700πcm²