The curved surface area of a cylinder is 264m2 and its volume is 524m3 Find the ratio of its - Maths - Surface Areas and Volumes

Question

The curved surface area of a cylinder is 264m2 and its volume is
524m3 Find the ratio of its diameter to its height

Manish Bharti · Accepted Answer

Let the diameter of cylinder be 'd'
We are given,
Curved surface area of cylinder $= 264 m^{2}$
$\Rightarrow 2 π r h = 264 \Rightarrow π d h = 264 - - - - (1)$
and
Volume of cylinder $= 524 m^{3}$
$\Rightarrow π r^{2} h = 524 \Rightarrow π \frac{(2 r)^{2}}{4} h = 524 \Rightarrow π d^{2} h = 4 \times 524 - - - - (2)$
dividing equ (2) by equ (1), we get
$\frac{π d^{2} h}{π d h} = \frac{4 \times 524}{264} d = \frac{262}{33}$
Substuting the value of d in equ (1), we get
$π \times \frac{262}{33} \times h = 264 \Rightarrow h = \frac{264 \times 33 \times 7}{262 \times 22} = \frac{1386}{131}$
therefore, ratio of diameter to the height of cylinder
$= \frac{\frac{262}{33}}{\frac{1386}{131}} = \frac{17, 161}{22, 869}$

The curved surface area of a cylinder is 264m2 and its volume is 524m3. Find the ratio of its diameter to its height