Question:
The sum of the radius of the base and height of a solid cylinder is $37 \mathrm{~m}$. If the total surface area of the solid cylinder is $1628 \mathrm{~cm}$. Find the volume of the cylinder.
Solution:
Given data is as follows:
h + r = 37 cm
Total surface area of the cylinder $=1628 \mathrm{~cm}^{2}$
That is,
$2 \pi r h+2 \pi r^{2}=1628$
2πr(h + 2r) = 1628
But it is already given in the problem that,
h + r = 37 cm
Therefore, 2πr × 37 = 1628
2 × 22/7 × r × 37 = 1628
r = 7 cm
Since, h + r = 37 cm
We have, h + 7 = 37 cm
H = 30 cm
Now that we know both height and radius of the cylinder, we can easily find the volume.
Volume $=\pi r^{2} h$
Volume = 22/7 × 7 × 7 × 30
Hence, the volume of the given cylinder is $4620 \mathrm{~cm}^{3}$.