The volume of an equilateral cylinder is 16п cm3. Find the area of the axial section.

The volume of any cylinder is found using the following formula:

V = πR²h, where R is the radius of the base of the cylinder, h is its height.

From the conditions of the problem it becomes clear that

R²h = 16.

Since the cylinder is equilateral, then

2R = h,

hence, the previous expression can be written like this:

R² * 2R = 16.

Let’s solve this equation:

R² * 2R = 16,

2R³ = 16,

R³ = 16/2,

R³ = 8,

R = 2 cm.

Hence, the height is

h = 2 * 2 = 4 cm.

In the axial section of an equilateral cylinder, there is a square, the sides of which are the diameter of the base and the height of the cylinder. Since they are equal to each other, the axial sectional area can be found by the formula:

S = h².

Find the area:

S = 4² = 16 cm².

Answer: the area of ​​the axial section of an equilateral cylinder is 16 cm².