Question

Which of the following can be used to calculate the volume of water inside the fish bowl?

Answer 1

The volume of a sphere can be calculated as

`V=(4)/(3)\pi r^3`

Where r is the radius of the sphere

We want to calculate half of the volume, then we must divide that volume by 2

`V^(\prime)=(1)/(2)(4)/(3)\pi r^3`

Now we must find the radius of our sphere, the segment AB is the diameter of the sphere, and the radius is half od the diameter, then

`r=(AB)/(2)=(12)/(2)=6`

Let's put it into our equation

`\begin{gathered} V^(\prime)=(1)/(2)\left((4)/(3)\right)(\pi)(r)^3 \\ \\ V^(\prime)=(1)/(2)\left((4)/(3)\right)(\pi)(6)^3 \end{gathered}`

The problem says to use

`\pi\approx(22)/(7)`

Then

`V^(\prime)=(1)/(2)\left((4)/(3)\right)\left((22)/(7)\right)(6)^3`

Final answer:

The formula that can be used to calculate the volume of water inside the fish bowl is

`V=(1)/(2)\left((4)/(3)\right)\left((22)/(7)\right)(6)^3`