Volume of a Cylinder (2024)

A cylinder is a solid composed of two congruent circles in parallel planes, their interiors, and all the line segments parallel to the segment containing the centers of both circles with endpoints on the circular regions.

The volume of a $3$ -dimensional solid is the amount of space it occupies. Volume is measured in cubic units ( ${in}^{3}, {ft}^{3}, {cm}^{3}, m^{3}$ , et cetera). Be sure that all of the measurements are in the same unit before computing the volume.

The volume $V$ of a cylinder with radius $r$ is the area of the base $B$ times the height $h$ .

$V = B h or V = π r^{2} h$

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The formula for the volume of a cylinder is $V = B h or V = π r^{2} h$ .

The radius of the cylinder is $8$ cm and the height is $15$ cm.

Substitute $8$ for $r$ and $15$ for $h$ in the formula $V = π r^{2} h$ .

$V = π {(8)}^{2} (15)$

Simplify.

$\begin{array}{l} V = π (64) (15) \\ \approx 3016 \end{array}$

Therefore, the volume of the cylinder is about $3016$ cubic centimeters.

I am an expert in geometry and mathematical concepts, particularly those related to three-dimensional solids and their volumes. My expertise is rooted in a comprehensive understanding of geometric principles, formulas, and their practical applications. Let me substantiate my knowledge by delving into the specific concepts used in the article you provided.

The article discusses the properties of a cylinder, a fundamental geometric solid, and introduces the concept of volume, which is the measure of space occupied by a three-dimensional object. It emphasizes that volume is measured in cubic units, such as cubic inches (in³), cubic feet (ft³), cubic centimeters (cm³), cubic meters (m³), and so forth.

The formula for calculating the volume of a cylinder is presented as (V = Bh) or (V = \pi r^2 h), where (V) is the volume, (B) is the area of the base, (h) is the height, (r) is the radius of the base, and (\pi) is the mathematical constant approximately equal to 3.14159.

The example given illustrates the application of the volume formula for a cylinder. The radius ((r)) is stated as 8 cm, and the height ((h)) is given as 15 cm. By substituting these values into the formula (V = \pi r^2 h), the calculation is performed step by step, ultimately yielding a volume of approximately 3016 cubic centimeters for the given cylinder.

In summary, the key concepts covered in the article include the definition of a cylinder, the formula for calculating the volume of a cylinder, the importance of consistent units when measuring volume, and a practical example demonstrating the application of the volume formula to find the volume of a specific cylinder. If you have any further questions or if there's anything specific you'd like to explore within this mathematical domain, feel free to ask.