If the heights of two circular cylinders are in the ratio 2 : 3 and their base radii are in the ratio 9:8, What is the ratio of their volumes?
A
27 : 32
B
27 : 23
C
23 : 32
D
21 : 27
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
\(\frac{h_1}{h_2}\) = \(\frac{2}{3}\)
h2 = \(\frac{2h_1}{3}\)
\(\frac{r_1}{r_2}\) = \(\frac{9}{8}\)
r2 = \(\frac{9r_1}{8}\)
v1 = \(\pi\)(\(\frac{9r_1}{8}\))2(\(\frac{2h_1}{3}\))
= \(\pi\)r1 2h1 x \(\frac{27}{32}\)
v = \(\frac{\pi r_1 2h_1 \times \frac{27}{32}}{\pi r_1 2h_1}\) = \(\frac{27}{32}\)
v2 : v1 = 27 : 32
Source: Myschool Past Questions Archive (Record #31480)