Question

Длина окружности в основании конуса 30 п см, а высота 10, найти объем конуса ​

Answer 1

Ответ:

750π см³

Объяснение:

С=2πR. →

R=C/2π=30π/2π=15см

Sосн=πR²=15²π=225π см ²

V=1/3*Sосн*h=1/3*225π*10=750π см³

Answer 2

Calculation of Cone Volume

To find the volume of a cone, we need to know the radius of the base and the height of the cone. In this case, we are given the circumference of the base, which can help us find the radius.

The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius. We are given that the circumference of the base is 30 cm. Using this information, we can calculate the radius as follows:

C = 2πr

30 = 2πr

Dividing both sides of the equation by 2π, we get:

r = 30 / (2π)

Now that we have the radius, we can proceed to calculate the volume of the cone.

The formula for the volume of a cone is V = (1/3)πr²h, where V is the volume, r is the radius, and h is the height.

In this case, we are given that the height of the cone is 10 cm. Substituting the values into the formula, we get:

V = (1/3)π(30 / (2π))²(10)

Simplifying the equation, we have:

V = (1/3)π(900 / (4π))(10)

Cancelling out the common factors, we get:

V = (1/3)(900 / 4)(10)

Simplifying further, we have:

V = (1/3)(225)(10)

Finally, calculating the volume, we get:

V = 750 cm³

Therefore, the volume of the cone is 750 cm³.