If the sum of radius and height of a cylinder is 21cm and its curved surface area is 616cm^2.Find T.S.A and volume of the cylinder.
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Radius of the cylinder = r
Height of the cylinder = h
According to the question :-
r+h = 21 cm - (1)
Curved Surface Area = 616 cm²
2πrh = 616
r×h = (616×7)÷(22×2)
r×h = 14×7
rh = 98 cm²
h = 98/r - (2)
On putting value of equation (2) in equation (1) :-
98/r+r = 21
(98+r²)/r = 21
98+r² = 21×r
r²-21r+98 = 0
On mid-term splitting :-
r²-7r-14r+98 = 0
r(r-7)-14(r-7) = 0
(r-7)(r-14) = 0
On considering one value as 'h' and other as 'r' we get :-
r = 7 cm
h = 14 cm
Total Surface Area = 2πr(r+h)
= 2×22/7×7(7+14)
= 2×22/7×7×21
= 2×22×21
= 924 cm²
Volume = πr²h
= 22/7×7×7×14
= 2156 cm²
The total surface area and volume of the cylinder are 924 cm² and 2156 cm² respectively.
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