A wedge of cheese is a sector of a cylinder. a. To the...

A wedge of cheese is a sector of a cylinder.
a. To the nearest tenth, what is the volume of the wedge with the dimensions shown?
b. What is the surface area of the wedge of cheese to the nearest tenth?
CAN'T COPY THE FIGURE

Key Concepts

Radian Measure and Arc Length

Understanding radian measure is crucial when dealing with sectors of circles or cylinders because many formulas, particularly for arc lengths and area of sectors, assume the angle is given in radians. The arc length of the curved edge is computed as the product of the radius and the central angle (in radians), and this concept is fundamental to partitioning the full circular shape.

Surface Area of a Cylindrical Sector

The surface area calculation incorporates both the areas of the flat surfaces (including the circular segments and the sector’s base or top) and the curved surface area that is a portion of the full cylinder’s lateral area. It may require computing the areas of the two radii faces, the arc face, and potentially the original circular face if it forms part of the external surface.

Sector of a Cylinder

This concept refers to a portion of a cylindrical solid that is carved out by radii spanning a given central angle. It involves understanding that the wedge or ‘sector’ represents a fraction of the full cylinder, which is determined by the ratio of the given central angle to a full rotation (360° or 2? radians).

Volume of a Cylindrical Sector

The volume of a cylindrical sector is calculated by taking the fraction of the full cylinder’s volume that corresponds to the sector's central angle. This involves first determining the volume of the complete cylinder (using the area of the base multiplied by the height) and then multiplying by the ratio of the sector’s angle to the full circle.

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