Question

The volume of a large can of tuna fish can be calculated using the formula V = πr2h. Write an equation to find the radius, r, in terms of V and h. Determine the diameter, to the nearest inch, of a large can of tuna fish that has a volume of 66 cubic inches and a height of 3.3 inches.

Answer 1

Answer:

The equation to find the radius, $r,$ in terms of $V$ and $h$ is $r = \sqrt{\frac{V}{\pi h}}$ .

The diameter of the large can of tuna fish  is 5 inches.

Step-by-step explanation:

Given:

volume of a large can of tuna fish $V=\pi r^2h$

We need to write the equation to find the radius, $r,$ in terms of $V$ and $h$.

Also we need to find the the diameter, to the nearest inch with volume of 66 cubic inches and a height of 3.3 inches.

Solution:

Now We know that;

$V=\pi r^2h$

So we can say that;

$r^2=\frac{V}{\pi h}\\\\r = \sqrt{\frac{V}{\pi h}}$

Hence The equation to find the radius, $r,$ in terms of $V$ and $h$ is $r = \sqrt{\frac{V}{\pi h}}$ .

Now we will find the diameter with volume of 66 cubic inches and a height of 3.3 inches.

So first we will find the radius by Substituting $V= 66\ in^3$ and $h =3.3\ in$

$r = \sqrt{\frac{V}{\pi h}}$

$r = \sqrt{\frac{66}{\pi \times 3.3}}\\\\r = 2.52\ in$

Now we know that;

Diameter is twice the radius.

So we get;

Diameter $d=2r=2\times2.52 =5.04\ in$

Rounding to nearest inch we get;

Diameter $d=5\ in$

Hence The diameter of the large can of tuna fish  is 5 inches.

Answer 2

1. An equation to find the radius, r, in terms of V and h is $r = \sqrt{\frac{V}{\pi h} }$

2. The diameter, to the nearest inch, of this large can of tuna fish is equal to 5.0 inches.

Given the following data:

• Volume of can = 66 cubic inches.

• Height of can = 3.3 inches.

1. To write an equation to find the radius, r, in terms of V and h:

Mathematically, the volume of a cylinder is given by this formula:

$V = \pi r^2h$

Making r the subject of formula, we have:

$r = \sqrt{\frac{V}{\pi h} }$

2. To determine the diameter, to the nearest inch, of this large can of tuna fish:

First of all, we would calculate the radius of this can as follows:

$r = \sqrt{\frac{66}{3.142 \times 3.3} }\\\\r=\sqrt{6.3654}$

Radius, r = 2.52 inches

Now, we can determine the diameter, to the nearest inch:

$Diameter = 2 \times radius\\\\Diameter = 2 \times 2.52$

Diameter = 5.04 ≈ 5.0 inches.

Read more on volume of a cylinder here: https://brainly.com/question/8913282