The base radius and height of a right circular cylinder is in the ratio of 1:7. If the volume is 176 cm3, the total surface area of the right circular cylinder is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\displaystyle\frac{1408}{7}\) cm2
The ratio gives the height in terms of the radius, so the volume \(\pi r^{2}h\) leaves only one unknown, \(r\). The total surface area of a cylinder is \(2\pi r(r+h)\): the curved surface plus the two circular ends.
Finding r and h (radius : height = 1 : 7, so \(h=7r\)):
\(\pi r^{2}(7r)=176\)
\(\displaystyle\frac{22}{7}\times7r^{3}=176\), that is, \(22r^{3}=176\)
\(r^{3}=8\), so \(r=2\,\mathrm{cm}\) and \(h=14\,\mathrm{cm}\)
Total surface area:
\(\displaystyle 2\pi r(r+h)=2\times\frac{22}{7}\times2\times(2+14)\)
\(\displaystyle =\frac{88\times16}{7}=\frac{1408}{7}\) cm2