A solid cylinder has total surface area of 462cm². It's curved surface area is one-third of its total surface area.find the radius and height of the cylinder
Answers
Answer:
Radius = 7 cm
Height = 3.5 cm
Step-by-step explanation:
To find :-
Radius of cylinder
Height of cylinder
From the question :-
total surface area of cylinder = 462 cm^2 (let it be x)
Surface area of curved part of cylinder = x * 1/3
= x/3
= 462 cm²/3
= 154 cm²
Surface area of two circles of the cylinder = x * 2/3
= 2x/3
= 2*462cm² /3
= 924cm² /3
= 308cm²
Surface area of one circle of cylinder = x * 2/2/3
= x * 1/3
= x/3
= 462 cm²/3
= 154 cm²
Solution :-
finding radius of the cylinder (r)-
154 cm² (area of one circular part of cylinder) = π*r*² (formula to find the area of circle)
154 cm² = 22/7 * r²
154*7/22 = r²
1078/22 = r²
49 = r²
√49 = r
7 cm = r
finding height of the cylinder (h)-
154 cm² (area of curved part of cylinder) = 2*π*r*h (formula to find the curved surface area of cylinder)
154 cm² = 2 * 22/7 * 7 cm * h
154 = 44/7 * 7 * h
154 = 308/7 * h
154*7/308 = h
154/44 (simplifying 7 with 308) = h
3.5 cm = h
Hence, the radius and height of cylinder are 7 cm and 3.5 cm respectively.