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.

 

Answer 1

$$\text{ Let r and h be the radius and height of the solid cylinder }.$$
$$\text{ Given: }$$
$$r+h=37m$$
$$\text{ Total surface area, }S=2\pi r(r+h)$$
$$1628=2\pi \times r\times 37$$
$$r=\frac{1628}{2\pi \times 37}$$
$$=\frac{1628}{232.477}$$
$$=7m$$
$$\text{ Circumference of its base },S_1=2\pi r$$
$$=(2\times \frac{22}{7}\times 7)m$$
$$=44m$$