Find the total surface area and lateral surface area of each of the following.
c) Length = 22 cm, Breadth = 17 cm and Height = 8 cm
Answers
Answer:
Given :-
Volume of cylinder= 2500π cm³
Height of cylinder= 49cm
To Find :-
We have to find the TSA and CSA of cylinder
Solution :-
\begin{gathered}\implies\sf\ TSA\ of\ cylinder= 2\pi r(h+r)\\ \\ \\ \sf\ CSA\ of\ cylinder= 2\pi r h\end{gathered}
⟹ TSA of cylinder=2πr(h+r)
CSA of cylinder=2πrh
Now ,
\begin{gathered}\implies\sf\ Volume\ of\ cylinder= \pi r^2 h\\ \\ \\ :\implies\sf\ \cancel{\pi} r^2\times 49= 2500\cancel{\pi} \\ \\ \\ :\implies\sf\ r^2= \dfrac{2500}{49}\\ \\ \\ :\implies\sf\ r= \sqrt{\dfrac{2500}{49}}\\ \\ \\ :\implies\underline{\boxed{\sf\ r=\dfrac{50}{7}}} \ cm\end{gathered}
⟹ Volume of cylinder=πr
2
h
:⟹
π
r
2
×49=2500
π
:⟹ r
2
=
49
2500
:⟹ r=
49
2500
:⟹
r=
7
50
cm
Find the CSA of cylinder
\begin{gathered}:\implies\sf\ CSA= 2\pi rh\\ \\ \\ :\implies\sf\ \ CSA= 2\times \dfrac{22}{7}\times \dfrac{50}{7}\times 49\\ \\ \\ :\implies\sf\ CSA= \dfrac{2\times 22\times 50\times \cancel{49}}{\cancel{7\times 7}}\\ \\ \\ :\implies\sf\ CSA= 44\times 50\\ \\ \\ \implies\underline{\boxed{\sf\ CSA=2200cm^2}}\end{gathered}
:⟹ CSA=2πrh
:⟹ CSA=2×
7
22
×
7
50
×49
:⟹ CSA=
7×7
2×22×50×
49
:⟹ CSA=44×50
⟹
CSA=2200cm
2
Now total surface area of cylinder
\begin{gathered}:\implies\sf\ TSA= CSA+ 2\times Area\ of\ circle\\ \\ \\ :\implies\sf\ TSA= 2\pi r h+ 2(\pi r^2)\\ \\ \\ :\implies\sf\ TSA= 2200+ \bigg(2\times \dfrac{22}{7}\times \dfrac{50}{7}\times \dfrac{50}{7}\bigg)\\ \\ \\ :\implies\sf\ TSA= 2200+\bigg(\dfrac{44\times 2500}{49}\bigg)\\ \\ \\ :\implies\sf\ TSA=2200+\bigg(\cancel{\dfrac{110000}{49}}\bigg)\\ \\ \\ :\implies\sf\ TSA= 2200+2244.89\\ \\ \\ :\implies\underline{\boxed{\sf\ TSA= 4444.89cm^2}}\end{gathered}
:⟹ TSA=CSA+2×Area of circle
:⟹ TSA=2πrh+2(πr
2
)
:⟹ TSA=2200+(2×
7
22
×
7
50
×
7
50
)
:⟹ TSA=2200+(
49
44×2500
)
:⟹ TSA=2200+(
49
110000
)
:⟹ TSA=2200+2244.89
:⟹
TSA=4444.89cm
2