Question

висота циліндра дорівнює 6 см, а діагональ осьового перерізу утворює з твірною кут 60°. знайти діагональ осьового перерізу циліндра та площу його основи​

Answer 1

Ответ:

d=h2+D2√=60.29925373

Объяснение:

Answer 2

Calculation of the Diagonal of the Axis Cross-Section of the Cylinder

To find the diagonal of the axis cross-section of the cylinder, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the diagonal of the axis cross-section of the cylinder forms a right triangle with the height of the cylinder (6 cm) and the radius of the cylinder's base. Since the diagonal forms a 60° angle with the radius, we can use trigonometric ratios to find the length of the diagonal.

Let's denote the radius of the cylinder's base as r and the length of the diagonal as d.

Using trigonometry, we can determine that the length of the diagonal is given by the equation:

d = 2r * sin(60°)

Now, let's substitute the given values into the equation and calculate the length of the diagonal.

r = 6 cm

d = 2 * 6 cm * sin(60°)

Using a calculator, we find that sin(60°) = 0.866.

d = 2 * 6 cm * 0.866

d ≈ 10.392 cm

Therefore, the length of the diagonal of the axis cross-section of the cylinder is approximately 10.392 cm.

Calculation of the Area of the Cylinder's Base

To find the area of the cylinder's base, we can use the formula for the area of a circle. The area of a circle is given by the equation:

A = πr^2

where A represents the area and r represents the radius of the circle.

In this case, the base of the cylinder is a circle with a radius of 6 cm.

Substituting the given value into the equation, we can calculate the area of the cylinder's base.

r = 6 cm

A = π * (6 cm)^2

Using the value of π as approximately 3.14159, we can calculate the area.

A = 3.14159 * (6 cm)^2

A ≈ 113.097 cm^2

Therefore, the area of the cylinder's base is approximately 113.097 cm^2.

I hope this helps! Let me know if you have any further questions.