Question

You’ve bought a cylindrical thermos 8 in. high with a base 6 in. across. How much coffee can you put in the thermos?

Answer 1

Answer: the liters translated to cubic inches is, 226.153996

Answer 2

3.706 liters

Explanation:

Hello

assuming that these measures correspond to the internal measures of the thermos,

we can calculate the volume as, the volume of a cylinder, which is given by

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

where r is the radius of the base, and h the height

also

Diameter=2r

r=Diameter/2

Step 1

let

h=8 in

base = diameter = 6 inch

r=diameter/2

r=6/2 inch,r=3 inch

Step 2

Put the values into the equation

`V=\pi r^(2) h\\V=\pi (3in)^(2) (8 in)\\V=\pi *72 \ in^(3) \\\\V=72\pi\ in^(3) \\\\`

Step 3

Now, the unit (cubic inches) is not an usual unit for measuring coffee, let´s convert cubic inches into liters by knowing

1 inch = 2.54 cm

1 litro = 1000 cubic centimeters

`if\ 1\ inch\ = 2.54\ cm\\(1\ inch)^(3) =(2.54\ cm)^(3)\\\\1\ inch^(3)=16.3870\ cm^(3)`

1 cubic inch = 16.3870 cubic centimeters

`1\ cubic\ inch\ = 16.3870\ cubic\ centimeters\\\\\\72\pi =x?\ cubic\ centimeters\\\\x=(72\pi \cubic \ inch\ \*16.3870 )/(1\ cubic\ inch) \\\\x=3706.65\ cubic\ centimeters`

Step 4

Finally, convert cubic centimeters into liters
`1000\ cubic\ centimeters =1\ liter \\\\\\3706.65\ cubic\ centimeters = x?\ liters\ centimeters\\\\x=(3706.65 \cubic \ centimeters\ \*1 liter)/(1000 cubic centimeters) \\\\x=3706.65\ cubic\ centimeters\\x=3.706 Liters`

I can put 3.706 liters in the thermos

Have a good day