Question

Calculate the volume of water in the cup when it is full

Answer 1

To find:

The volume of the water in the cup when it is full.

Solution:

The volume of the water is equal to the difference of the volume of the small cone and the larger cone.

Here, the ratio of the radius of both cones is equal to the ratio of their heights. SO,

$\begin{gathered} \frac{r}{2.7}=\frac{20}{20-8} \\ \frac{r}{2.7}=\frac{20}{12} \\ \frac{r}{2.7}=\frac{5}{3} \\ r=4.5 \end{gathered}$

The radius of the larger cone is 4.5 cm.

So, the volume of the water is:

$\begin{gathered} V=\frac{1}{3}\pi R^2H-\frac{1}{3}\pi r^2h \\ =\frac{1}{3}\pi(R^2H-r^2h) \\ =\frac{1}{3}\pi((4.5)^2(20)-(2.7)^2(12)) \\ =\frac{1}{3}\cdot\frac{22}{7}(405-87.48) \\ =\frac{22}{21}(317.52) \\ =332.64cm^2 \end{gathered}$

The volume of water when the cup is full is 332.64 cm^2.