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The ratio between the curved surface area and total surface area of a right circular cylinder is 1:2. Find the ratio between the height and radius of the cylinder.
Given:
The ratio between the curved surface area and total surface area of a right circular cylinder is 1:2.
To do:
We have to find the ratio between the height and radius of the cylinder.
Solution:
We know that,
Curved surface area of a right circular cylinder of height $h$ and radius $r=2\pi rh$.
Total surface area of a right circular cylinder of height $h$ and radius $r=2\pi rh+2\pi r^2=2\pi r(h+r)$.
Let the height of the right circular cylinder be $h$ and radius be $r$.
Therefore,
$2\pi rh:2\pi r(h+r)=1:2$
$h:(h+r)=1:2$
$2h=1(h+r)$
$2h-h=r$
$h=r$
$h:r=h:h=1:1$
Therefore, the ratio between the height and radius of the cylinder is $1:1$.
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