The volume of a right circular cylinder (think of a pop can) is jointly proportional to the square of the radius of the circular base and to the height. For example, when the height is 10.62 cm and the radius is 3 cm, then the volume is 300 cm3.

Find the formula of the volume of a cylinder using the following variables: V = volume, h = height, r = radius. Describe how you found the constant in the formula you have given.

Using the formula you just discovered, find the volume to the nearest tenth of a cylinder with radius 4 cm and height 15.92 cm

An open top box with a square base is to be constructed from two types of materials,one for the bottom and one for the sides. The volume of the box is to be a cubic feet. The cost of the bottom is php 4 per square, foot and the cost of material for the side is php 3 per square foot.Let be the length of the edge of the square base and let y be the height of the open box

To find the formula for the volume of a right circular cylinder, let's start by defining the variables:

V = volume of the cylinder
h = height of the cylinder
r = radius of the circular base of the cylinder

According to the problem, the volume (V) is jointly proportional to the square of the radius (r^2) and to the height (h).

Therefore, we can write the formula as follows:

V = k * r^2 * h

Where k is the constant of proportionality.

To find the value of the constant (k), we can use the given information that when the height is 10.62 cm and the radius is 3 cm, the volume is 300 cm^3.

Plugging these values into the formula, we get:

300 = k * 3^2 * 10.62

Simplifying this equation, we have:

300 = k * 9 * 10.62

Dividing both sides by (9 * 10.62), we get:

k = 300 / (9 * 10.62)

Evaluating the right-hand side gives:

k ≈ 3.53982

So, the formula for the volume of a cylinder is:

V = 3.53982 * r^2 * h

Now, let's use this formula to find the volume of a cylinder with a radius of 4 cm and a height of 15.92 cm:

V = 3.53982 * 4^2 * 15.92

V ≈ 903.7696

Therefore, the volume of the cylinder, to the nearest tenth, is approximately 903.8 cm^3.

To find the formula for the volume of a cylinder, we are given that the volume is jointly proportional to the square of the radius (r^2) and the height (h). Therefore, we can write the formula as:

V = k * r^2 * h

where V represents the volume, r is the radius, h is the height, and k is the constant of proportionality that we need to determine.

To find the value of k, we can use the given information about the volume when the height is 10.62 cm and the radius is 3 cm, which is 300 cm^3. Plugging these values into the formula, we get:

300 = k * 3^2 * 10.62

Simplifying, we get:

300 = k * 9 * 10.62
300 = 95.58k

Now we can solve for k by dividing both sides of the equation by 95.58:

k = 300 / 95.58
k ≈ 3.14

Therefore, the formula for the volume of a cylindrical can be written as:

V = 3.14 * r^2 * h

Now let's use this formula to find the volume of a cylinder with a radius of 4 cm and a height of 15.92 cm. Plugging these values into the formula, we get:

V = 3.14 * 4^2 * 15.92
V ≈ 1005.44 cm^3

So, the volume of the cylinder is approximately 1005.44 cm^3 to the nearest tenth.

Oh well, I'll play

300 = k * 3^2 * 10.62
so
k = 300/(9*10.62) = 3.14
remarkable :)

in fact v = pi r^2 h
= pi * 3^2 * 10.62
= 300.27 :)

so we say
v = 3.14 * r^2 *h
= 3.14 * 16 * 15.92
=785 cm^3