The total surface area of a cylinder is 4092 cm2 and the diameter of its base is 21 cm. What is one-third of the volume of the cylinder, to the nearest whole number? (Take \(\pi=\frac{22}{7}\))
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 5948 cm3
The total surface area of a cylinder is \(2\pi r(r+h)\): the curved surface plus the two circular ends. With the radius known it gives the height, and then the volume is \(\pi r^2h\).
Radius \(=21\div2=10.5\) cm, so \(\displaystyle 2\pi r=2\times\frac{22}{7}\times10.5=66\)
\(66(10.5+h)=4092\), so \(10.5+h=62\) and \(h=51.5\) cm
Volume \(\displaystyle =\frac{22}{7}\times10.5\times10.5\times51.5=346.5\times51.5=17844.75\) cm3
One-third \(=17844.75\div3=5948.25\approx5948\) cm3
