Question

Цилиндр и конус имеют общие основание и высоту. Объем конуса меньше объёма цилиндра на 12. Найдите объем цилиндра.

Answer 1

Ответ:

18 ед³

Пошаговое объяснение:

Объем конуса    $\displaystyle V_k=\frac{\pi r^2h}{3};$

объем цилиндра $\displaystyle V_c =\pi r^2h$.

И разница составляет 12 единиц³.

Запишем это и найдем :

$\displaystyle \pi r^2h - \frac{\pi r^2h}{3} =12;\qquad 2\pi r^2h = 36;\qquad \boldsymbol {\pi r^2h = 18}$

тогда объем цилиндра

$\displaystyle V_c =\pi r^2h = 18$ (ед³)

ответ

объем цилиндра 18 ед³

Answer 2

Finding the Volume of the Cylinder

To find the volume of the cylinder, we need to use the information given in the question. The cylinder and cone have a common base and height, and the volume of the cone is 12 units less than the volume of the cylinder.

Let's assume the radius of the base of both the cylinder and the cone is r and the height is h.

The volume of a cylinder is given by the formula: V_cylinder = π * r^2 * h. The volume of a cone is given by the formula: V_cone = (1/3) * π * r^2 * h. According to the question, the volume of the cone is 12 units less than the volume of the cylinder. Mathematically, this can be expressed as:

V_cylinder - V_cone = 12

Substituting the formulas for the volumes of the cylinder and cone, we get:

π * r^2 * h - (1/3) * π * r^2 * h = 12

Simplifying the equation, we have:

(2/3) * π * r^2 * h = 12

Now, we can solve for the volume of the cylinder by rearranging the equation:

V_cylinder = (3/2) * 12 = 18

Therefore, the volume of the cylinder is 18 cubic units.

Please let me know if you need any further assistance!