Question

A= hlba)10. The volume of a large can of tuna fish can be calculated using the formula V = ar?h.Write an equation to find the radius, r, in terms of V and h. Determine the diameter, tothe nearest inch, of a large can of tuna fish that has a volume of 66 cubic inches and aheight of 3.3 inches.

Answer 1

Given the formula for volume:

`V\text{ = }\pi r^2h`

Let's rewrite the formula in terms r, V and h.

i) Rewriting for r in terms of V and h :

`\begin{gathered} V\text{ = }\pi r^2h \\ (V)/(h)=\pi r^2 \\ \\ \sqrt[]{(V)/(\pi h)}=r \\ \\ r\text{ = }\sqrt[]{(V)/(\pi h)} \end{gathered}`

2) Given:

Volume, V = 66 cubic inches

height, h = 3.3 inches

We know that diameter is radius multiplied by 2.

To find the diameter, first find the radius.

Therefore, we have:

`\begin{gathered} r\text{ = }\sqrt[]{(V)/(\pi h)} \\ \\ r\text{ = }\sqrt[]{(66)/(3.3\pi)} \\ \\ r\text{ = }2.52\text{ inches} \end{gathered}`

Since the radius is 2.52 inches, the dia,eter will be:

D = r x 2 = 2.52 x 2 = 5.04 inches

To the nearest inch = 5 inches

ANSWER:

diameter = 5 inches