The ratio between the curved surface Area and the total surface area of a cylinder is 1:2 find the volume of the cylinder given that the total surface area is 616 cm cube
Answers
Answer:
1078 cm cube
Step-by-step explanation:
curved surface area : total surface area => 1 : 2
=> total surface area = 616 cm^2
let
sum of CSA & TSA be x
so
TSA = x × 2/3 => 616 = 2x/3
=> 2x = 616 × 3
=> x = 616 × 3/2 = 924
so
CSA = 924 × 1/3 = 308 cm^2
now
CSA = 2πrh & TSA = 2πr(r+h)
=> CSA : TSA = 1 : 2
=> 2πrh : 2πr(r+h) = 1 : 2
=> 2(2πrh) = 1(2πr(r+h)
=> 2h = r+h
=> h = r
&
CSA = 2πrh
= 2 × 22/7 × {r}^2 = 308
=> {r}^2 = 308 × 7 / 44
=> {r}^2 = 49
=> r = √49 = 7
given
now
volume of cylinder = π(r)^2h
=> volume = π × r × r × h
=> volume = π × (r) ^3
=> volume = 22/7 × (7)^3
=> volume = 1078 cm cube
Answer:
given csa:tsa =1:2
therefore tsa = 2×csa
tsa = 616 cm²
TSA = 2πr (h + r)
CSA = 2πrh
csa:tsa = 1:2
2πrh : 2πr(h+r) = 1:2
(2πrh)/(2πr(h+r) = 1/2
(h) /(h+r) = 1/2 [on cancelling 2πr on both num. and den.]
2h = h+r
2h-h = r
h = r
so height and the radius are equal
tsa = 616cm²
2πr(h+r)=616cm²
2πr(r+r) = 616 [as h=r]
2πr(2r) = 616
4πr² = 616
πr² = 616/4
r² = 154/π
r² = 49
r = 7
hence r=h=7cm
volume of cylinder = πr²h
= π7²×7 = π7³
= 22/7 × 7³
= 22×7²
=1078cm³