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# Calculate The Volume of A Cylindrical Wedge

Last updated: Saturday, April 29, 2023
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Cylindrical Wedge

A cylindrical wedge is a fascinating three-dimensional geometric figure obtained by cutting a cylinder using a plane that intersects the base of the cylinder. This unique shape, which can be envisioned as a portion of a cylinder, has various applications in mathematics, engineering, design, and even in culinary arts. The study of cylindrical wedges provides insights into geometry and the interplay between different shapes, enabling creative exploration in both theoretical and practical applications.

Real-life examples of objects with a shape similar to a cylindrical wedge can be found in a range of settings, highlighting the versatility and appeal of this geometric figure. In culinary arts, a slice of a cylindrical cake or a piece of cheese from a wheel showcases the cylindrical wedge shape, offering both visual appeal and portion control. In engineering, gears or mechanical components may be designed with cylindrical wedge shapes to optimize contact and improve torque transmission.

In the world of architecture and design, cylindrical wedge-shaped elements can be incorporated into furniture, sculptures, or structural components to create a unique visual effect and maximize the efficient use of space. This shape can also be found in nature, as tree rings or cross-sections of certain fruits and vegetables exhibit the characteristics of a cylindrical wedge, demonstrating the diverse applications and fascinating properties of this geometric form.

Easily calculate the volume of a cylindrical wedge with step-by-step guidance using our free calculator below.

The formula for determining the volume of a cylindrical wedge is defined as:
$$V$$ $$=$$ $$\dfrac{h_w \cdot r^2}{3}$$ $$\cdot$$ $$\dfrac{3 \cdot \sin(\theta_1) - 3 \cdot \theta \cos(\theta_1) - sin^3(\theta_1) }{1 - \cos(\theta_1)}$$
$$V$$: the volume of the cylinder
$$r$$: the radius of the circular base
$$h_w$$: the height of the wedge
$$\theta_1$$: the angle between the base segment height and the radius
The SI unit of volume is: $$cubic \text{ } meter\text{ }(m^3)$$

## Find $$V$$

Use this calculator to determine the volume of a cylindrical wedge using the radius of the cylinder, the height of the wedge and the angle.
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the radius of the circular base
$$r$$
$$meter$$
the height of the wedge
$$h_w$$
$$meter$$
the angle between the base segment height and the radius
$$\theta_1$$
$$degree$$
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