Question:
The sum of the radius of the base and height of a solid cylinder is 37 m. If the total surface area of the solid cylinder is 1628 m2, find the circumference of its base.
Solution:
Let $r$ and $h$ be the radius and height of the solid cylinder.
Given :
$r+h=37 \mathrm{~m}$
Total surface area, $S=2 \pi r(r+h)$
$1628=2 \pi \times r \times 37$
$\mathbf{r}=\frac{1628}{2 \pi \times 37}$
$=\frac{1628}{232.477}$
$=7 \mathrm{~m}$
Circumference of its base, $S_{1}=2 \pi \mathrm{r}$
$=\left(2 \times \frac{22}{7} \times 7\right) \mathrm{m}$
$=44 \mathrm{~m}$