Question

2. How much water could my well hold if the depth of the well is 30ft and the diameter of the well is 24ft?

Answer 1

`13,571.68\text{ ft}^3\approx 384307.18\text{ liters}`

Explanation:

We are asked to find the amount of water that the well can hold.

We will use volume of cylinder formula to solve our given problem.

`V=\pi r^2 h`, where,

V = Volume of cylinder,

r = Radius,

h = Height.

`d=2r`

`24=2r`

`12=r`

`V=\pi (12\text{ ft})^2* 30\text{ ft}`

`V=\pi*144 \text{ ft}^2* 30\text{ ft}`

`V=4,320\pi \text{ ft}^3`

`V=13,571.68026\text{ ft}^3`

`V\approx 13,571.68\text{ ft}^3`

Since our given volume is in cubic feet, so we can convert it in liters by multiplying 13,571.68 by 28.3168.

`\text{Water in well}=13,571.68\text{ ft}^3*\frac{28.3168\text{ liter}}{ \text{ ft}^3}`

`\text{Water in well}=384,307.180556\text{ liter}`

Therefore, the well could hold approximately 384307.18 liters of water.

Answer 2

`V=4,320\pi\ ft^(3)` or
`V=13,564.8\ ft^(3)`

Explanation:

we know that

The volume of the cylinder (the well) is equal to

`V=\pi r^(2) h`

where

`r=24/2=12\ ft` ----> the radius is half the diameter

`h=30\ ft`

substitute

`V=\pi (12)^(2)(30)`

`V=4,320\pi\ ft^(3)`

assume

`\pi =3.14`

`V=4,320(3.14)=13,564.8\ ft^(3)`