How to Determine the Width of a Lamp with Parabolic Shape
What shape does a lamp have when viewed from the side?
A lamp has the shape of a parabola when viewed from the side.
How is the width of the lamp calculated?
Based on the data provided, how can the width of the lamp be determined?
Shape of the Lamp
When viewed from the side, the lamp has the shape of a parabola. This unique geometric shape plays a crucial role in determining its width.
Calculating the Width
The width of the lamp can be calculated by understanding the relationship between the light source (focus) and the bottom of the lamp, as well as the depth of the lamp.
Understanding the Parabolic Shape of the Lamp
A parabola is a curve where any point is at an equal distance from a fixed point (focus) and a fixed straight line (directrix). In the case of the lamp, the focus represents the light source, while the directrix is not explicitly mentioned.
By knowing that the light source is centimeters from the bottom of the lamp, we can deduce that the distance from any point on the parabola to the focus is also centimeters. This characteristic helps in determining the lamp's width.
Calculation of Lamp Width
The depth of the lamp, which indicates the distance from the bottom to the top of the parabolic shape, is mentioned as centimeters. Since the distance from any point on the parabola to the focus is also centimeters, the width of the lamp can be calculated as twice the depth, resulting in centimeters.