Question

a small cup has a hight of 6 in, and a large cup has a hight of 8 in. The large coffe holds 18oz. How much coffe is in the small cup​

Answer 1

Given:-

• A small cup has height of 6in. and a large cup has a height of 8in.
• Volume of coffee in large cup is 18oz .

To find:-

• The volume of coffee small cup .

Answer:-

Here we can assume the shape of the cup to be cylindrical . And the volume of a cylinder is given by;

`\implies V = \pi r^2 h \\`

where ,

• 
  `r` is the radius of the base of the cylinder.
• 
  `h` is the height of the cylinder.

Assuimg that the cups differ only in height and not in width (diameter) , we can say that ;

`\implies V \propto h \\`

So , we can write;

`\implies (V_s)/(V_l)=(h_s)/(h_l)\\`

`\implies (V_s)/(18\ oz)=(6\ in.)/(8 \ in.)\\`

`\implies V_s = (6(18))/(8) \\`

`\implies \underline{\underline{ V_s =13.5 \ oz}} \\`

Hence the volume of the smaller cup is 13.5 oz .

and we are done!