Question

Цилиндр и конус имеют общее основание и высоту. Объём цилиндра равен 90. Найдите объём конуса.

Answer 1

V(цил)= П*R^2*hV(кон)= 1\3*П*R^2*hТо есть цилиндр в 3 раза больше конуса, следовательно получается 10*3= 30 

Answer 2

Problem Analysis

We are given that a cylinder and a cone have a common base and height. The volume of the cylinder is given as 90. We need to find the volume of the cone.

Solution

To find the volume of the cone, we need to know the formula for the volume of a cone. The formula for the volume of a cone is given by:

Volume of Cone = (1/3) * π * r^2 * h

where: - π is a mathematical constant approximately equal to 3.14159 - r is the radius of the base of the cone - h is the height of the cone

Since the cylinder and the cone have a common base and height, the radius and height of the cone will be the same as that of the cylinder.

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

Given that the volume of the cylinder is 90, we can use the formula for the volume of a cylinder to write the equation:

Volume of Cylinder = π * r^2 * h = 90

Now, we can substitute the value of the volume of the cylinder and solve for the volume of the cone.

Calculation

Let's solve the equation to find the value of the volume of the cone.

π * r^2 * h = 90

We are given that the volume of the cylinder is 90, so we can substitute this value into the equation:

π * r^2 * h = 90

Now, we can solve for the volume of the cone by dividing both sides of the equation by 3:

(1/3) * π * r^2 * h = (1/3) * 90

Simplifying the equation:

Volume of Cone = (1/3) * 90

Volume of Cone = 30

Therefore, the volume of the cone is 30.

Answer

The volume of the cone is 30.