Question

Consider a hollow cylinder of inner radius $r$ and thickness of wall $t$ and length $l$. The volume of the above cylinder is given by

• A. $2\pi lt(r^2-l^2)$
• B. $2\pi rlt(\frac{t}{2r}+1)$
• C. $2\pi lt(r^2+l^2)$
• D. $2\pi rlt(r+t)$

Answer 1

Answer: (B)

$2\pi rlt(\frac{t}{2r}+1)$

Required volume= Total volume of the cylinder with radius $r+t$ $-$ volume of the cylinder with radius $r$

$=\pi (r+t{)}^{2}l-\pi r^{2}l$
$=\pi l\left[\right(r+t{)}^2-r^2]$

$=\pi l(2r+t)t$
$=2\pi rlt(\frac{t}{2r}+1)$