Question

В цилиндр вписан шар объемом 10,найти объем цилиндра

Answer 1

Вы­со­та ци­лин­дра равна диа­мет­ру шара, а ра­ди­ус ос­но­ва­ния ци­лин­дра равен ра­ди­у­су шара. Обьем шара Vш=4/3*пи*R³, R³=3Vш/4пи=30/4пи=15/2пи. Обьем цилиндра Vц=пиR²h=пиR²*2R=2пиR³=2пи*15/2пи=15.

Answer 2

Calculating the Volume of a Cylinder

To find the volume of a cylinder when a sphere is inscribed in it, we can use the formula for the volume of a cylinder and the volume of a sphere.

The formula for the volume of a cylinder is given by: V_cylinder = π * r^2 * h Where: - V_cylinder is the volume of the cylinder - π is a constant approximately equal to 3.14159 - r is the radius of the cylinder - h is the height of the cylinder

The formula for the volume of a sphere is given by: V_sphere = (4/3) * π * r^3 Where: - V_sphere is the volume of the sphere - π is a constant approximately equal to 3.14159 - r is the radius of the sphere

Solution

Given that the volume of the inscribed sphere is 10, we can find the radius of the sphere and then use it to calculate the volume of the cylinder.

The radius of the sphere can be found using the formula: V_sphere = (4/3) * π * r^3 Solving for r, we get: r = (3 * V_sphere / (4 * π))^(1/3)

Substituting the given volume of the sphere (10) into the formula, we get: r = (3 * 10 / (4 * π))^(1/3)

Now that we have the radius of the sphere, we can use it to find the volume of the cylinder using the formula: V_cylinder = π * r^2 * h

This will give us the volume of the cylinder.

Let's calculate the volume of the cylinder using the given information.