The total surface area of a solid cylinder 165cm\(^2\). Of the base diameter is 7cm, calculate its height. [Take \(\pi = \frac{22}{7}\)]
A
7.5 cm
B
4.5 cm
C
4.0 cm
D
2.0 cm
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
165 = 2 x \(\frac{22}{7}\) x \(\frac{7}{2}\) x h + 2 x \(\frac{22}{7}\) x \(\frac{7}{2}\) x \(\frac{7}{2}\)
165 = 22h + 77
\(\frac{22h}{22} = \frac{88}{22}\)
height = 4cm
Source: Myschool Past Questions Archive (Record #57228)