The radius and height of a cylinder are in the ratios 5:7 and it's volume is 550cm^3. Find it's radius.

Question

It's a question of surface area and volumes for class 9th

Answer 1

Given a ratio of 5:7 we can use 5 units for the radius and 7 units for the height.

 

Assuming a radius of 5 units and a height of 7 units, The area of the cylinder base is Pi*5*5 = 3.14159*25 = 78.54

 

Then

 

Vol = A * H = 78.54 * 7 = 549.78 cubic units

 

Which is very close to 550

 

So it seems that the units we selected are equal to centimeters. 

 

There is a more appropriate algebraic solution that someone else can provide for you.

 

 

 

Answer 2

Let radius = r

Let height = h

 

r / h = 5 / 7          eq1

 

h = (7 / 5)r           eq1   ----> rewritten

 

V = πr²h                 eq2   ---> volume

 

 

Plug in the known volume and substitute the value of h into the volume equation.

 

550 = πr²(7/5)r

 

550 = (7/5)πr³

 

 

Solve for r from this equation.

 

Multiply both sides of the equation by 5/(7π).

 

 

(550 * 5) / (7π) = πr³

 

2750 / (7π) = πr³

 

 

Divide both sides of the equation by π.  Then cube-root the result to get your radius.