Question

Обчисліть обєм та площу бічної поверхні циліндра з висотою 5 см і радіусом основи 2 см та конуса з такою ж висотою і основою такого самого радіуса

Answer 1

Обєм=2*П*2^2*5=40П см куб

Площа поверхн=2*П*2*5=20Псм.кв

Обэм конуса= 40п/3 см куб

Площа поверхны=П*2*(корень с(25-4)=2корень с 21П

Answer 2

Calculation of the Cylinder's Volume and Surface Area

To calculate the volume and surface area of a cylinder, we need to know its height and the radius of its base. In this case, the height of the cylinder is 5 cm, and the radius of the base is 2 cm.

The formula for the volume of a cylinder is given by:

Volume of Cylinder = π * r^2 * h

where π is a mathematical constant approximately equal to 3.14159, r is the radius of the base, and h is the height of the cylinder.

Substituting the given values into the formula, we can calculate the volume of the cylinder:

Volume of Cylinder = 3.14159 * 2^2 * 5 = 62.8318 cm^3.

The formula for the lateral surface area of a cylinder is given by:

Lateral Surface Area of Cylinder = 2 * π * r * h

Substituting the given values into the formula, we can calculate the lateral surface area of the cylinder:

Lateral Surface Area of Cylinder = 2 * 3.14159 * 2 * 5 = 62.8318 cm^2.

Calculation of the Cone's Volume and Surface Area

To calculate the volume and surface area of a cone, we also need to know its height and the radius of its base. In this case, the height of the cone is 5 cm, and the radius of the base is 2 cm.

The formula for the volume of a cone is given by:

Volume of Cone = (1/3) * π * r^2 * h

Substituting the given values into the formula, we can calculate the volume of the cone:

Volume of Cone = (1/3) * 3.14159 * 2^2 * 5 = 20.9433 cm^3.

The formula for the lateral surface area of a cone is given by:

Lateral Surface Area of Cone = π * r * l

where l is the slant height of the cone. The slant height can be calculated using the Pythagorean theorem:

l = sqrt(r^2 + h^2)

Substituting the given values into the formula, we can calculate the slant height of the cone:

l = sqrt(2^2 + 5^2) = sqrt(29) cm.

Substituting the slant height into the formula for the lateral surface area, we can calculate the lateral surface area of the cone:

Lateral Surface Area of Cone = 3.14159 * 2 * sqrt(29) = 36.6529 cm^2.

To summarize: - The volume of the cylinder is approximately 62.8318 cm^3. - The lateral surface area of the cylinder is approximately 62.8318 cm^2. - The volume of the cone is approximately 20.9433 cm^3. - The lateral surface area of the cone is approximately 36.6529 cm^2.

Please note that these calculations assume the measurements are accurate and the shapes are perfect.