The total surface area of a solid right circular cylinder is 1617 $$cm^{2}$$. If the diameter of its base is 21 cm, then what it its volume (in $$cm^{3}$$) (Taken $$\pi=\frac{22}{7}$$)

If the diameter of its base is 21 cm.

radius = r = $$\frac{21}{2}$$ = 10.5 cm

The total surface area of a solid right circular cylinder is 1617 $$cm^{2}$$.

$$2\times\ \pi\ \times\ radius\times\ \left(radius+height\right) = 1617$$

$$2\times\ \frac{22}{7}\times\ 10.5\times\ \left(10.5+height\right) = 1617$$

$$44\times\ 1.5\times\ \left(10.5+height\right) = 1617$$

$$66\times\ \left(10.5+height\right) = 1617$$

$$\left(10.5+height\right) = 24.5$$

height = 24.5-10.5

= 14

Volume = $$\pi\times\left(radius\right)^2\times height$$

= $$\frac{22}{7}\times\left(10.5\right)^2\times14$$

= $$22\times110.25\times2$$

= 4851 $$cm^{3}$$