The base radius of a cylinder is 5 m more than its height. If the curved surface area of the cylinder is 792 m2, then what is the volume of the cylinder (in m3) ? (Use \(\pi=\displaystyle\frac{22}{7}\))
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 5544
The curved surface area \(2\pi rh\) gives the product of the radius and the height; with \(r=h+5\) this becomes a quadratic in the height. Once \(r\) and \(h\) are known, volume \(=\pi r^2h\).
Finding r and h (curved surface area 792 m2):
From the curved surface area: \(2\times\displaystyle\frac{22}{7}\times rh=792\), so \(rh=126\)
The radius is 5 m more than the height: \(h(h+5)=126\), so \(h^2+5h-126=0\)
Factorising: \((h+14)(h-9)=0\), so \(h=9\) m (a height cannot be negative)
The radius, 5 m more than the height: \(r=9+5=14\) m
Volume:
\(V=\displaystyle\frac{22}{7}\times14\times14\times9=44\times14\times9=5544\,\mathrm{m^3}\)