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An electronics company is designing the packaging for its latest model of tablet computer.
The tablet is shaped like a rectangular prism that is 23.5 centimeters long, 15.5 centimeters
wide, and 0.7 centimeters thick. It will be packaged in a box shaped like a rectangular prism.
To protect the device, the rest of the volume in the box will be filled with foam material so
that there is at least 1 centimeter of foam on all sides of the tablet.
What is the least possible volume of foam the company could use to package one tablet?
Round your answer to the nearest cubic centimeter.
cubic centimeters

Respuesta :

To find the least possible volume of foam the company could use to package one tablet, we need to consider the dimensions of the tablet and the space required for foam padding around it.

1. Calculate the dimensions of the box that will contain the tablet with the foam padding:

- Length: 23.5 cm + 2(1 cm) = 25.5 cm (additional 1 cm on each end)

- Width: 15.5 cm + 2(1 cm) = 17.5 cm (additional 1 cm on each side)

- Height: 0.7 cm + 2(1 cm) = 2.7 cm (additional 1 cm on top and bottom)

2. Calculate the volume of the box:

Volume = Length x Width x Height

Volume = 25.5 cm x 17.5 cm x 2.7 cm

Volume ≈ 1210.125 cm³

3. Calculate the volume of the tablet:

Volume of tablet = Length x Width x Height

Volume of tablet = 23.5 cm x 15.5 cm x 0.7 cm

Volume of tablet ≈ 254.075 cm³

4. Calculate the volume of foam needed:

Volume of foam = Volume of box - Volume of tablet

Volume of foam = 1210.125 cm³ - 254.075 cm³

Volume of foam ≈ 956.05 cm³

Therefore, the least possible volume of foam the company could use to package one tablet is approximately 956 cubic centimeters.