an electronic manufacturer wants to ship a stereo system. The system includes the following components:
1 Receiver 20in. x 8in.
1 CD Player 20in. x 8in. x 5in.
1 Dual Tape Deck 20in. x 8in. x 6in.
2 Half-Cylinder Speakers, each with a height of 22 in. and a radius of 4 in.
To keep the components secure, all remaining space in the box must be filled with packing filler. What is the aproximate number of cubic inches of filler needed to pack one box?
To calculate the approximate number of cubic inches of filler needed to pack one box, we need to find the volume of the box and subtract the volume of the components.
Here's how we can do it step by step:
1. Calculate the volume of each individual component.
- Receiver: 20in. x 8in. = 160in²
- CD Player: 20in. x 8in. x 5in. = 800in³
- Dual Tape Deck: 20in. x 8in. x 6in. = 960in³
- Half-Cylinder Speaker: Since a half-cylinder is a semicircle on top of a rectangle, we need to calculate the volume separately for the rectangular part and the semicircular part.
- Rectangular part: height x width x depth = 22in. x 4in. x 8in. = 704in³
- Semicircular part: π * radius² * height/2 = π * (4in.)² * 22in./2 = 176πin³ (approximately 552in³)
2. Sum up the volumes of all the components.
160in² + 800in³ + 960in³ + 704in³ + 552in³ = 3176in³
3. Calculate the volume of the box.
The box has dimensions of 20in. x 8in. x (height + 22in.), so the volume is 20in. x 8in. x (22in. + 22in.) = 20in. x 8in. x 44in. = 7040in³
4. Calculate the volume of the filler needed.
7040in³ (box volume) - 3176in³ (component volume) = 3864in³
Therefore, the approximate number of cubic inches of filler needed to pack one box is 3864in³.