Question

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 1

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

`\begin{gathered} V=(1)/(3)\pi r^2h \\ \pi=3.14 \\ r=5 \\ h=8 \\ V=(628)/(3)\approx209.33 \end{gathered}`

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

`(1)/(4)V=(1)/(4)\cdot(628)/(3)=(157)/(3)\approx52.33`

Since each sphere has a radius of 0.5:

`\begin{gathered} \text{Let:} \\ x=\text{Number of shots} \\ (628)/(3)-0.5x=(628)/(3)-(157)/(3) \\ \text{solve for x:} \\ 0.5x=(628)/(3)-157 \\ 0.5x=(157)/(3) \\ x\approx100 \end{gathered}`