Question

Cylinder figure:-
Height = 20m, L.S.A (Lateral Surface Area) = 2640m^2 . Find Radius and T.S.A (Total Surface Area) then.


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Answer 1

Analysis→

Here we're given that the height of a cylinder is 20m. And the LSA(Lateral Surface Area) of the cylinder is 2640m². And we've to find the radius and the TSA(Total 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→

• Height of Cylinder=20m
• LSA of Cylinder=
• Assuming pi( $\pi$ )= $\rm\dfrac{22}{7}$

To Find→

Radius and TSA of the cylinder.

Answer→

$\maltese$ First let's find the radius with the help of the given LSA of the cylinder.

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

$\implies\rm{2640m^2=2\times\dfrac{22}{7}\times r\times20m}$

$\implies\rm{2640m^2=\dfrac{880}{7}m\times r}$

$\implies\rm{2640\times7m^2=880m\times r}$

$\implies\rm{r=\dfrac{2640\times7m^2}{880m}}$

$\implies\rm{r=\dfrac{18480m^2}{880m}}$

$\implies\rm{r=\dfrac{\cancel{18480m^2}}{\cancel{880m}}}$

$\implies\rm{r=21m}$

${\underline{\boxed{\implies{\bf{r=21m\checkmark}}}}}$

_________________________

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

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

${\implies{\rm{TSA=2\times\dfrac{22}{7}\times21m(21m+20m)}}}$

${\implies{\rm{TSA=2\times\dfrac{22}{\cancel{7}}\times\cancel{21m}(21m+20m)}}}$

$\implies\rm{TSA=2\times22\times3m\times41m}$

$\implies\rm{TSA=44\times123m^2}$

$\implies\rm{TSA=5412m^2}$

${\boxed{\boxed{\bf{\therefore TSA\:of\:cylinder=5412m^2\checkmark}}}}$

☞ Hence the radius of the cylinder is 21m and its total surface area is 5412m² which is the required answer.

HOPE IT HELPS.

Answer 2

Answer:

GIVEN

Height = 20m

L.S.A (Lateral Surface Area) = 2640m²

TO FIND

Radius and T.S.A (Total Surface Area)

SOLUTION

L.S.A = 2640

2πrh = 2640

22/7×r×20 = 1320

r = (1320×7)/(22×20)

r = 21 m

TSA = 2πr(r + h)

= 2 × 22/7 × 21 (21 + 20)

= 2 × 22 × 3 × 41

= 44 × 123

= 5412 m²

Step-by-step explanation: