Question

(ROTATE !!!!!!!) help plssss i’ll give a lot of points for being quick

Answer 1

(a) -
`V_(tank)\approx 2010.6 \ yd^3`

(b) -
`Total= 1005 \ \text{fish}`

Explanation:

Given the cylindrical fish tank with a diameter of 16 yards and a height of 10 yards. We are asked to answer the following.

(a) - How much water can the tank hold, in other words what is the tank's volume?

(b) - Given that a specific kind of fish requires 2 yd³ of water per fish, find the total amount of fish that can occupy the tank.

Part (a):

Given:

`d=16 \ yd\\h=10 \ yd`

Find:

`V_(tank)= \ ?? \ yd^3`

For part (a) the question is essentially asking what the volume of the tank is, the tank is a cylinder. We can use the following formula to find the volume of a cylinder.

`\boxed{\left\begin{array}{ccc}\text{\underline{Volume of a Cylinder:}}\\\\V=\pi r^2h\end{array}\right}`

(1) Find the radius of the tank given that the diameter is 10 yards

`r=(d)/(2)\\\\ \Longrightarrow r=((16 \ yd))/(2) \\\\\therefore \boxed{r=8 \ yd}`

(2) - Compute the volume of the tank using the formula from above and the value of the radius we just found.

`V_(tank)=\pi r^2h\\\\\Longrightarrow V_(tank)=\pi (8 \ yd)^2(10 \ yd)\\\\ \Longrightarrow V_(tank)=\pi (64 \ yd^2)(10 \ yd)\\\\\Longrightarrow V_(tank)=640\pi\\\\\therefore \boxed{\boxed{V_(tank)\approx 2010.6 \ yd^3}}`

Thus, the volume of the tank is found.

Part (b):

Given:

`V_(tank)=2010.6 \ yd^3\\V_(1 \ fish)= 2 \ yd^3`

Find:

`\text{Total}= \ ?? \ \text{fish}`

To find the total amount of fish that can fit in the tank, simply divide the total volume of the tank by the volume one fish requires.

`Total=(V_(tank))/(V_(1 \ fish)) \\\\\Longrightarrow Total=(2010.6 \ yd^3)/(2 \ yd^3)\\\\\therefore \boxed{\boxed{Total= 1005 \ fish}}`

Thus, the tank can hold 1005 fish.