Answered

A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere with a radius of 0.5 cm, are dropped into the vessel, one fourth of the water flows out. Find the number of lead shots dropped in the vessel. Use n =3.14 O 50 75 O 80 O 100 complete water

Answer :

First, let's find the volume of the cone:

[tex]\begin{gathered} V=\frac{1}{3}\pi r^2h \\ \pi=3.14 \\ r=5 \\ h=8 \\ V=\frac{628}{3}\approx209.33 \end{gathered}[/tex]

Let's find how much is the fourth of the water:

[tex]\frac{1}{4}V=\frac{1}{4}\cdot\frac{628}{3}=\frac{157}{3}\approx52.33[/tex]

Since each sphere has a radius of 0.5:

[tex]\begin{gathered} \text{Let:} \\ x=\text{Number of shots} \\ \frac{628}{3}-0.5x=\frac{628}{3}-\frac{157}{3} \\ \text{solve for x:} \\ 0.5x=\frac{628}{3}-157 \\ 0.5x=\frac{157}{3} \\ x\approx100 \end{gathered}[/tex]

Go Question: Other Questions