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
Answers
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
Step-by-step explanation:
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