The total surface area of a cylinder is 4092 cm² and the diameter of its base is 21 cm. What is \(\frac{1}{3}\)rd of the volume (in cm³) of the cylinder (nearest to an integer)?

5948 cm³

Total surface area of a cylinder= 2\(\pi \)r (r + h)

d = 21 and r = \(\frac{21}{2}\)

2 × \(\frac{22}{7}\) × \(\frac{21}{2}\) (\(\frac{21}{2}\) + h) = 4092

h = 62 - \(\frac{21}{2}\) = \(\frac{103}{2}\) cm

volume = \(\pi \)r²h = \(\frac{22}{7}\) × \(\frac{21×21}{2×2}\) × \(\frac{103}{2}\)

\(\frac{1}{3}\)rd of the volume= \(\frac{1}{3}\) × \(\frac{22}{7}\) × \(\frac{21×21}{4}\) × \(\frac{103}{2}\) = 5948.25 cm³

Nearest to an integer = 5948 cm³