Question

you are pouring canned soda into a cylinder cylinder that is 12 cm tall and a diameter of 6.5 cm The picture is 36 cm tall and has a diameter of 20 cm how many cans of soda will the picture hold

Answer 1

We are going to assume that the picture of 36 tall and has a diameter of 20 cm is also a cylinder.

To answer this question, we need to know the formula to find the volume of a cylinder:

`V_{\text{cylinder}}=\pi\cdot r^2\cdot h`

Where

• r is the radius of the base of the cylinder.

,

• h is the height of the cylinder.

,

• pi = 3.14159265358979...

From the question, we have:

The dimensions of the first cylinder are:

h = 12cm

D = 6.5cm.

Since the radius of a circle is half of its diameter, then, we have that the radius of this cylinder is 6.5cm/2 = 3.25cm.

Then, r = 3.25cm.

Then, the volume of this cylinder is:

Now, we need to find the volume of the cylinder of the picture following the same procedure:

h = 36cm

D = 20cm ---> r = D/2 ---> r = 20cm/2 ---> r = 10cm

Then, we have that the volume of the cylinder of the picture is:

`V_{\text{cylinderpicture}}=3600\pi cm^3`

Thus, we have that we poured a canned soda into a cylinder of 147pi cm^3. How many cans of soda will hold the cylinder of the picture? We need to divide the total volume of the cylinder of the picture by the volume of the first cylinder (the one which contains the canned soda). Then, we have:

`N_{\text{cannedsoda}}=\frac{V_{\text{cylinderpicture}}}{V_{\text{cylinder}}}=(3600\pi cm^3)/(126.75\pi cm^3)\Rightarrow N_(cannedsoda)=28.402367`

Therefore, the cylinder of the picture will hold about 28.40 canned sodas.