Question

plzz help me.i m stuck. ​

Answer 1

For this we have to find whose volume among the hemisphere and the cone was the least. Didn't the glass with the least one contain more quantity of juice?

The hemisphere of the first glass

Here the radius of the hemisphere was the same as the inner radius of the first glass, i.e.,

$\sf{r_1=3\ cm}$

Then the volume of the hemisphere was,

$\sf{V_1=\dfrac{2}{3}\pi(r_1)^3}\\\\\\\sf{V_1=\dfrac{2}{3}\pi(3)^3}\\\\\\\sf{V_1=\dfrac{2}{3}\pi\times27}\\\\\\\sf{V_1=18\pi\ cm^3$

The cone in the second glass

Here, $\sf{h=1.5\ cm.}$

As in the first glass, the base radius of the cone was the same as the inner radius of the second glass, i.e.,

$\sf{r_2=3\ cm}$

Then the volume of the cone was,

$\sf{V_2=\dfrac{1}{3}\pi(r_2)^2h}\\\\\\\sf{V_2=\dfrac{1}{3}\pi(3)^2\times1.5}\\\\\\\sf{V_2=\dfrac{1}{3}\pi\times9\times1.5}\\\\\\\sf{V_2=4.5\pi\ cm^3}$

We can see that $\sf{V_2\ \textless\ V_1,}$ i.e., the volume of the cone was lesser than that of the hemisphere.

This means the second glass with the conical bottom could hold more quantity of juice than the first glass with the hemispherical bottom, since the heights of both the glasses were same.

Hence Isha's father Suresh got more quantity of juice.

But by how much?

$\sf{V_1-V_2=(18\pi-4.5\pi)\ cm^3}\\\\\\\sf{V_1-V_2=13.5\pi\ cm^3}\\\\\\\sf{V_1-V_2=13.5\pi\ ml}$

Hence, Suresh got 13.5 ml more quantity of juice than Isha.