Question

Cylinder figure:-
Radius = 28m , T.S.A (Total Surface Area) = 5805m^2
Find height and L.S.A (Lateral Surface Area) then.

Formula for L.S.A of a cylinder =
$2\pi \: rh$
Formula for T.S.A of a cylinder
=
$2\pi \: r \: (r + h)$
​

Answer 1

Answer:

formula for L.S.A of cylinder= 2×22/7×r×h

Formula for TSA of cylinder=22/7×r^2×h

Answer 2

Analysis→

Here we're given that the radius of a cylinder is 28m and its TSA(total surface area) is 5805m². And we've to find the radius and the LSA(lateral surface area) or the cylinder. And we know that :

${\dashrightarrow{\bf{LSA\:of\:cylinder=2\pi rh}}}$

${\dashrightarrow{\bf{TSA\:of\:cylinder=2\pi r\big(r+h\big)}}}$

Given→

• Radius of cylinder=28m
• TSA of cylinder= 5805m²
• Assuming ( $\pi$ )= $\rm\dfrac{22}{7}$

To Find→

Height and LSA of the cylinder.

Answer→

$\maltese$ First let's find the height from the given TSA of the cylinder.

$\implies\rm{TSA=2\pi r\big(r+h\big)}$

${\implies{\rm{5805m^2=2\times\dfrac{22}{7}\times28m\big(28m+h\big)}}}$

${\implies{\rm{5805m^2=2\times\dfrac{22}{\cancel{7}}\times\cancel{28m}\big(28m+h\big)}}}$

${\implies{\rm{5805m^2=2\times22\times4m\big(28m+h\big)}}}$

${\implies{\rm{5805m^2=176m\big(28m+h\big)}}}$

$\implies\rm{\big(28m+h\big)=\dfrac{5805m^2}{176m}}$

$\implies\rm{\big(28m+h\big)=\dfrac{\cancel{5805m^2}}{\cancel{176m}}}$

$\implies\rm{\big(28m+h\big)=32.982m}$

$\implies\rm{\big(28m+h\big)≈33m}$

$\implies\rm{h=5m}$

${\underline{\boxed{\implies{\bf{h=5m\checkmark}}}}}$

_________________________

$\maltese$ Now we've found the height of the cylinder, so let's find its lateral surface area ahead »

$\implies\rm{LSA=2\pi rh}$

$\implies\rm{LSA=2\times\dfrac{22}{7}\times28m\times5m}$

$\implies\rm{LSA=2\times\dfrac{22}{\cancel{7}}\times\cancel{28m}\times5m}$

$\implies\rm{LSA=2\times22\times4m\times5m}$

$\implies\rm{LSA=44\times20m^2}$

$\implies\rm{LSA=800m^2}$

${\boxed{\boxed{\bf{\therefore LSA\:of\:cylinder=880m^2\checkmark}}}}$

☞ Hence the height the of the cylinder is 5m and its LSA is 880m² which is the required answer.

HOPE IT HELPS.