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Now multiply the area of the circle by the length of the cylinder. 16π × 10 = 160π. Using the S⇔D calculator button, this is 502۰6548246. Using the approximation π = 3۰142, the calculation is 50۰272 × 10 = 502۰72. This value now needs to be rounded.

The total surface area of the cylinder is two circle areas, 2 × π𝒓², plus the curved surface area of the rectangle, 2π𝒓 × 𝒉. This gives the formula, surface area = 2π𝒓² + 2π𝒓𝒉.

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The area of the curved surface (the rectangle) is 2πr × 𝒉. The radius is 5 m and the height is 9 m. When using the π button, the area of the curved rectangular face is 2 × π × 5 × 9 = 90π m². When using the approximation π = 3۰142, the area is 2 × 3۰142 × 5 × 9 = 282۰78 m².

Work out the volume of the cylinder, giving the answer to the nearest whole number. Use the π button on a calculator or the approximation π = 3۰142

Gas cylinder

A good understanding of calculations for the circumference of a circle and the area of a circle is useful when calculating the surface area and volume of a cylinderclosecylinderA 3D shape with a constant circular cross-section across its length..

Firstly, work out the area of the cross-section of the cylinder (a circle). Using π on a calculator, the area of the cross-section is π × 4² = 16π. Using the approximation π = 3۰142, the area of the cross-section is 3۰142 × 4² = 50۰272

The volumeclosevolumeThe amount of space occupied by a 3D shape, measured in cubic units, such as cm³, mm³ and m³. May also be referred to as capacity. of a cylinder is the areacloseareaA measure of the size of any plane surface or 2D shape. Area is measured in square units, for example, square centimetres or square metres: cm² or m². of its cross-section, a circle, multiplied by its height. Volume is measured in cubic units, such as cm³ or m³.

The total surface area closesurface area (of a 3D shape)The total area of all the faces of a 3D shape. Measured in square units, such as cm² and m². of a cylinder is made up of two circular facesclosefaceOne of the flat surfaces of a solid shape. and a curved surface which makes a rectangle if flattened out. Surface area is measured in square units, such as cm² and m².

Certain foods, such as baked beans, vegetables, fish and meat, are commonly sold in cylinder-shaped tins. Cylinders pack efficiently into boxes for shipping, taking up approximately 90% of the available space.

cylinder翻译

The radius of the circular cross-section is 5 m. The area of one circular face is πr². When using the π button on the calculator, the area of both circular faces is 2 × π × 5² = 50π m². When using the approximation π = 3۰142, the area of both circular faces is 2 × 3۰142 × 5² = 157۰1 m².

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A cylinder is made up of two congruent circles and a rectangle. The circles are the top face and the base face of the cylinder. The circles are directly opposite each other. The rectangle is the curved face around the cylinder.

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To make the tins accurately, manufacturers need to calculate the surface area plus a small amount of extra area for the seams. The volume of the cylinder shape will determine the quantity of food that can go inside a tin.

A cylinder is made up of two congruentclosecongruentShapes that are the same shape and size, they are identical. circles that are directly opposite one another, and a rectangle.

Work out the surface area of the cylinder. Use π = 3۰142 or the π button on a calculator. Give the answer to 3 significant figures.

Cylindrical

To work out the surface area, the radius and the height of the cylinder are used. Each circle has the radius, 𝒓. The rectangle’s length is the circumference of the circular cross-section, this is 2π𝒓 or π𝒅. The width of the rectangle is the height of the cylinder, 𝒉.

cylinder中文

Their circular cross-section also means that the tins can withstand pressure when stored. The food contained in them has a long shelf life.

cylinder发音

Substitute the value of the radius, 𝒓 = 10, and the height, 𝒉 = 20, into the formula 𝑽 = π𝒓²𝒉, and work out the calculation. 3۰142 × 10² × 20 = 6284. The volume of the cylinder is 6284 mm³.

\(r\) is the radius of the circular cross-section and \(h\) is the height of the cylinder.If the diameter, \(d\), of the circular cross-section is given, this is halved to find the radius.

The formula for the volume of a cylinder uses height. Length can be used in place of height as they are the same dimension.

Cylindricalsurfaces with a common axis

The diameter of the circular cross-section is 8 cm. The radius is half of the diameter. The radius, 𝒓, is 4 cm. The length of the cylinder is 10 cm. The length can also be described as the height, 𝒉, of the cylinder.

A cylinder is a 3Dclose3DThree-dimensions: length, width and height. shape with a circular cross-sectionclosecross-sectionThe face that results from slicing through a solid shape. .

Cylindricalcoordinates

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cylinder气缸

This is given by the formula \(V\) = π\(r\)²\(h\) , where \(r\) is the radius of the circular cross-section and \(h\) is the height of the cylinder.

Calculations may be carried out numerically using a decimal approximation for πcloseπ (pi)Pi is used to represent the ratio of a circumference of a circle to its diameter, denoted with the Greek symbol π (pi), such as 3۰14 or 3۰142. Workings may also be written symbolically in terms of π. This means that the result is given as a multiple of π.

Practise working out the surface area and volume of cylinders with this quiz. You may need a pen and paper to help you with your answers.

The answer 140π can also be given as a decimal using the S⇔D button on a calculator. This button is used to convert a value in terms of π to a decimal value. This gives 439۰8229715, which rounds to 440 m² to 3 significant figures.

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Imagine that a solid cylinder is sliced open. The face that is revealed is called the cross-section. The cross-section of a cylinder is a circle. The cross-section is the same all the way through the cylinder.

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Sum the areas of the circles and the rectangle. 50π + 90π = 140π. When using the π button, the total surface area of the cylinder is 140π m². When using the approximation π = 3۰142, the total surface area is 157۰1 + 282۰78 = 439۰88 m².

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