the ratio of the curved surface area to the total surface area of a right circular cylinder is 1:2. find the volume of the cylinder, if its total surface area is 616 cm2.
Answers
2πrh / 2πr(r+h) = 1/2
h/(r+h) = 1/2
by cross multiplication, we get
2h = r+h
2h-h = r
therefore h=r
by calculating, we get height is equal to radius. then ratio of their height and radius is
height of cylinder : radius of cylinder = 1:1
We have curved surface area= 2π*r*h
we have the circular surface area= 2πr²
ATQ 2πr(h+r)= 616 ---(1)
and 2*2πrh= 2πrh+ 2πr²
⇒ h=r
Substituting value of h in (1)
we have 4πr²=616
⇒ r²=59
⇒ r=7
Volume of the cylinder is
⇒ πr².h= πr³
⇒ = πr³=1078cm³We have curved surface area= 2π*r*h
we have the circular surface area= 2πr²
ATQ 2πr(h+r)= 616 ---(1)
and 2*2πrh= 2πrh+ 2πr²
⇒ h=r
Substituting value of h in (1)
we have 4πr²=616
⇒ r²=59
⇒ r=7
Volume of the cylinder is
⇒ πr².h= πr³
⇒ = πr³=1078cm³We have curved surface area= 2π*r*h
we have the circular surface area= 2πr²
ATQ 2πr(h+r)= 616 ---(1)
and 2*2πrh= 2πrh+ 2πr²
⇒ h=r
Substituting value of h in (1)
we have 4πr²=616
⇒ r²=59
⇒ r=7
Volume of the cylinder is
⇒ πr².h= πr³
⇒ = πr³=1078cm³