the ratio between the curved surface and total surface of a cylinder is 1:2. find the volume of the cylinder , given that its total surface area is 616cm
Answers
Answered by
521
if TSA is 616 sq.cm, then CSA will be 616/2 = 308 sq.cm. (ratio is 1:2)
TSA = 2*22/7*r*h + 2*22/7*r*r
substituting 2*22/7*r*h as CSA, we get 308 + 2*22/7*r*r = 616 sq.cm
therefore, 2*22/7*r*r = 616-308 = 308
therefore, 2*22/7*r*r = 308
r*r = (308*7) / (2*22)
r*r = 49, r = 7 cm
to find h,
2*22/7*7*h = 308 sq.cm. (CSA)
44h = 308, h = 308/44
h = 7cm
now, volume = 22/7*r*r*h
= 22/7*7*7*7
volume of cylinder is 1078 cubic. cm
TSA = 2*22/7*r*h + 2*22/7*r*r
substituting 2*22/7*r*h as CSA, we get 308 + 2*22/7*r*r = 616 sq.cm
therefore, 2*22/7*r*r = 616-308 = 308
therefore, 2*22/7*r*r = 308
r*r = (308*7) / (2*22)
r*r = 49, r = 7 cm
to find h,
2*22/7*7*h = 308 sq.cm. (CSA)
44h = 308, h = 308/44
h = 7cm
now, volume = 22/7*r*r*h
= 22/7*7*7*7
volume of cylinder is 1078 cubic. cm
Answered by
618
hello...
here's ur answer...
the CSA and TSA of the cylinder are in ratio of 1:2, if the TSA of the cylinder is 616cm² then the CSA will be=616/2
=308cm²
CSA of the cylinder=308cm²
2πrh/2πr(h+r)=1/2
h/h+r=1/2
h+r=2h
h=r
Curved surface area = 2πrh = 2πr²= 308 [Since h = r]
2πr²=308cm²
2×22/7×r²=308cm²
44/7×r²=308cm²
r²=308/1×7/44
r²=49
r=√49
r=7cm
therefore height of the cylinder will also be 7cm
volume of the cylinder=πr²h
=22/7×7×7×7
=22×7×7
=1078cm³
hope this helps...
here's ur answer...
the CSA and TSA of the cylinder are in ratio of 1:2, if the TSA of the cylinder is 616cm² then the CSA will be=616/2
=308cm²
CSA of the cylinder=308cm²
2πrh/2πr(h+r)=1/2
h/h+r=1/2
h+r=2h
h=r
Curved surface area = 2πrh = 2πr²= 308 [Since h = r]
2πr²=308cm²
2×22/7×r²=308cm²
44/7×r²=308cm²
r²=308/1×7/44
r²=49
r=√49
r=7cm
therefore height of the cylinder will also be 7cm
volume of the cylinder=πr²h
=22/7×7×7×7
=22×7×7
=1078cm³
hope this helps...
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