Question

Two paint cans are similar right cylinder as shown below. If the volume of the larger paint can is 9600 cubic centimetre, find the volume of the smaller paint can.

Answer 1

720.85 cm3

Explanation:

As the cylinders are similar, the ratio of their diameters is the same ratio of their heights, so we have that:

d1 /d2 = h1 / h2

If the volume of the larger cylinder is 9600 cm3, we can find its height:

V = pi*r^2 * h

9600 = pi * 32^2 * h

h = 9600 / (pi * 32^2) = 2.9842 cm

Now we find h2:

64 / 27 = 2.9842 / h2

h2 = 27 * 2.9842 / 64 = 1.259 cm

Finally, we can find the volume of the smaller cylinder:

V = pi * r^2 * h

V = pi * 13.5^2 * 1.259 = 720.85 cm3

Answer 2

The volume of the smaller paint can is 720.85
`cm^(3)`.

Explanation:

Since the two paint cans are similar, the dimensions of their diameters and heights are in a definite proportion.

The volume of a cylinder =
`\pi`
`r^(2)`h

Since the diameter of the larger paint can is 64 cm, the radius =
`(diameter)/(2)`

=
`(64)/(2)`

= 32 cm

Given that the volume is 9600 cubic centimetre, the height of the larger paint can could be determined by;

V =
`\pi`
`r^(2)`h

9600 =
`(22)/(7)` ×
`32^(2)` × h

9600 = 3218.2857 h

⇒ h = 2.983 cm

Two cylinders are similar if their diameter and height are proportional.

Let
`d_(1)` represent the diameter of the larger paint can,
`d_(2)` the diameter of the smaller paint can,
`h_(1)` the height of the larger paint can and
`h_(2)` the height of the smaller paint can. So that;

`(d_(1) )/(d_(2) )` =
`(h_(1) )/(h_(2) )`

`(64)/(27)` =
`(2.983)/(h_(2) )`

⇒
`h_(2)` = 1.2585

`h_(2)` = 1.3 cm

If the diameter of the smaller paint can is 27, then its radius = 13.5 cm. So that its volume cane be determined by;

volume =
`\pi`
`r^(2)`h

=
`(22)/(7)` ×
`(13.5)^(2)` ×1.2585

= 720.8508

= 720.85
`cm^(3)`

The volume of the smaller paint can is 720.85
`cm^(3)`.