Question

Цилиндр описан около шара.объем шара-8см кубических.найдите объем цилиндра

Answer 1

Объём шара равен:

Vш=4πr³/3 

выразим радиус:

r³ = 3Vш/4π

 

Объём цилиндра:

V=Sосн*H

Sосн = πr²

H=2r

V=2πr³

 

V=2π*3Vш/4π = 3Vш / 2 = 3*8/2 = 12 см³

Answer 2

Объём шара находится по формуле 4/3 Пи R в кубе. Имеем 8=4/3*П*R3, следовательно R3=6/П. Объём цилиндра равен  Пи умноженное на радиус  в квадрате  и на высоту V=П * R2*H, но радиус цилиндра равен радиусу шара, а высота - диаметру, т.е. двум радиусам. Имеем V=П*R2*2R= 2*П*R3. Подставляем вместо R3 6/П, V=2*П*6/П, П сократятся и V=12 куб.см.

Answer 3

Finding the Volume of a Cylinder Inscribed in a Sphere

To find the volume of a cylinder inscribed in a sphere, we need to know the volume of the sphere. In this case, the volume of the sphere is given as 8 cubic centimeters.

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

Step 1: Find the radius of the sphere. The formula for the volume of a sphere is V = (4/3)πr^3, where V is the volume and r is the radius. Rearranging the formula, we can solve for the radius: r = (3V / (4π))^(1/3).

Substituting the given volume of the sphere (V = 8 cubic centimeters) into the formula, we can calculate the radius.

Step 2: Calculate the radius of the sphere. r = (3 * 8 / (4 * π))^(1/3).

Now, let's calculate the radius using the formula.

Step 3: Find the volume of the cylinder. The volume of a cylinder is given by the formula V = πr^2h, where V is the volume, r is the radius, and h is the height of the cylinder.

Since the cylinder is inscribed in the sphere, the height of the cylinder will be equal to the diameter of the sphere.

Step 4: Calculate the volume of the cylinder. V = πr^2h.

Now, let's substitute the calculated radius and the diameter of the sphere into the formula to find the volume of the cylinder.

Calculation:

Step 1: Find the radius of the sphere. r = (3 * 8 / (4 * π))^(1/3).

Using a calculator, we can find the value of r.

Step 2: Calculate the radius of the sphere. r ≈ 0.879 cm.

Step 3: Find the volume of the cylinder. V = πr^2h.

Since the cylinder is inscribed in the sphere, the height of the cylinder will be equal to the diameter of the sphere. Therefore, the height of the cylinder is 2r.

Step 4: Calculate the volume of the cylinder. V = π(0.879)^2(2 * 0.879).

Using a calculator, we can find the value of V.

Answer:

The volume of the cylinder inscribed in the sphere is approximately 4.86 cubic centimeters.