Question

The total surface area of a right circular cylinder is 462 cm square.If its curved surface area is on-third of its total surface area, find the valume of the cylinder.

Answer 1

total surface area = 2 x area of circle + area of curve surface
a/c to question ,
curve surface area=1/3 x total surface area
so,
3 x curve surface area =2 x circle area+curve surface area

2 x curve surface area =2 x circle area
2 x 2pi.r .h = 2 x pi.r^2
h=r/2

again ,
2/3 total surface area = area of circle
2/3 x 462=pi.r^2
2 x 154 = 22/7 x r^2

r=7root2 cm
so,
h=7/root2

now,
volume =pi.r^2.h=22/7 x 7 x 7 x 2 x 7/root2
=1078 root2 cm^3

Answer 2

TSA of cylinder=462 sq cm
2πrh+πr2=462
also,CSA of cylinder=1/3*462=154 sq cm (2πrh)-------1
⇒2πrh=154-------2
154+22r2/7=462           (from1)
1078+22r2=3234
22r2=3234-1078
r2=98----------3
r=9.89    put in 2
2*22/7*9.89*h=154
⇒h=2.47 cm
Volume of cylinder =πr2h
⇒22/7*98*2.47=760.76 cm3-----------Ans
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