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)?
Answer & explanation
Correct answer: option 2
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