Select a cylindrical shape below

The surface area of a cylindrical wedge is the sum of its lateral surface area plus both the base and top surface areas. A cylindrical wedge is created from a cylinder by slicing it with a plane that intersects the base.

The formula for determining the surface area of a cylindrical wedge is defined as:

\(SA\) \(=\) \(A_l\) \(+\) \(A_t\) \(+\) \(A_b\)

\(where\)

\(A_l\) \(=\) \(2\) \(\cdot\) \(h_w\) \(\cdot\) \(r\) \(\cdot\) \(\Big(\dfrac{\sin(\theta_1) - \theta_1 \cdot \cos(\theta_1)}{1 - \cos(\theta_1)}\Big)\)

\(A_t\) \(=\) \(h_{t1}\) \(\cdot\) \(r\) \(\cdot\) \(cos^{-1}(1\) \(-\) \(\dfrac{h_t}{h_{t1}})\) \(-\) \(h_{t1}\) \(\cdot\) \(r\) \(\cdot\) \((1\) \(-\) \(\dfrac{h_t}{h_{t1}})\) \(\cdot\) \(\sqrt{\dfrac{2 \cdot h_t}{h_{t1}} - \dfrac{h_t^2}{h_{t1}^2}}\)

\(A_b\) \(=\) \(r^2\) \(\cdot\) \(\Big(\dfrac{2\theta_1 \cdot \pi}{360^\circ}\) \(-\) \(\dfrac{\sin(2\theta_1)}{2}\Big)\)

\(SA\): the surface area of the cylinder

\(A_l\): the lateral surface area of the wedge

\(A_t\): the area of the top elliptical segment

\(A_b\): the area of the base circular segment

\(r\): 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 surface area is: \(square \text{ } meter\text{ }(m^2)\)

## Find \(SA\)

Use this calculator to determine the surface area of a cylindrical wedge when the height of the base circular segment is greater or equal to the base radius.

Hold & Drag

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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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