Question:
The curved surface area of a cylinder is 264 m2 and its volume is 924 m3. The ratio of its diameter to its height is
(a) 3 : 7
(b) 7 : 3
(c) 6 : 7
(d) 7 : 6
Solution:
The C.S.A. of cylinder
S = 264 m2
The volume of cylinder
V = 924 m3
$2 \pi r h=264$
....................(i)
$2 r h=84$
$r h=42$
$\pi r^{2} h=924$
...........$. .(i i)$
$r(r h)=42 \times 7$
From eq. (i) and (ii),
We get $r=7$
Putting the value in $(i) \quad h=6$
Hence, $\frac{d}{h}=\frac{14}{6}=\frac{7}{3}$
$d: h=7: 3$
Hence, the correct answer is choice (b).