Question in description as no space sorry.

Question

Calculate the volume of a cylinder of height 7 cm and diameter 7 cm what will be in the change in the volume of the cylinder if the diameter is doubled and the height is halved?

Answer 1

V = pi*radius^2*height

pi = 22/7

 

height = 7 and radius = 3.5 

V = pi * 3.5^2 * 7 =

 

      (22/7)*3.5^2 * 7

    = 22*3.5^2 = 269.5 <--- 7 cancels

 

 

Diameter is doubled and height is halved....

 Diameter is now 14 ---> radius is 7

 height is now 3.5

 

 V = 22/7 * 7^2 * 3.5 = 22*7*3.5 = 539

 

Change in volume is 539 - 269.5 =  269.5

 

So the volume doubles as expected.

 

Here's a quick proof that this will ALWAYS happen

when you double the radius and halve the height.

 

V = pi*R^2*H  <--- volume of the cylinder

 

Doubles the radius and halves the height

H' = H/2  

R' = 2*R

 

The volume is now V' = pi*H' * R' ^2  =

 

                                = pi * (H/2) * (2R)^2  <--- substitutes R' = 2*r and h' = H/2

 

                               = pi * H/2 * 4 * r^2  <---- squares the monomial

 

                                 = pi * H * 2 * r^2  <---- 4 cancels the 2

 

                                 = 2 * pi*r^2 * h  <--- commutative property of multiplication

                         

                                 = 2 * (pi*r^2*h) <--- associative property of multiplication

 

                                 = 2 * V  <--- substitutes the original volume

 

[end of proof]