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Answer:
No. The den will have 8 times the volume of the bedroom.
Step-by-step explanation:
The architect wants the bedroom to have the dimensions of 8 ft by 4 ft by 7 ft. Let's find the volume of the bedroom:
8 * 4 * 7 = 224 cubic feet
The architect doubles all three dimensions to create the den. This means that the den has dimensions as 16 ft by 8 ft by 14 ft.
The volume of the den is:
16 * 8 * 14 = 1792 cubic feet
Double of 224 cubic feet is 448 cubic feet.
Hence, the den will not have double the volume of the bedroom instead it will have a volume 8 times the that of the bedroom.
Doubling the initial dimensions of 8 ft. by 4 ft. by 7 ft. means that the
volume will 8 times the initial volume or 1,792 ft.
What is the scale factor of volume be used?
The dimensions of the room = 8 ft. by 4 ft. by 7 ft.
The amount by which the architect increases the dimension = Double the dimensions
Solution;
The volume of the room, V = 8 ft. × 4 ft. × 7 ft. = 224 ft.³
When the dimensions are doubled, we have;
Length = 2 × 8 ft. = 16 ft.
Width = 2 × 4 ft. = 8 ft.
Height = 2 × 7 ft. = 14 ft.
The new volume of the bedroom = 16 ft. × 8 ft. × 14 ft. = 1792 ft.³
Therefore;
- The volume of the bedroom after doubling the dimension will be 1,792 ft.³
Scale factor of volume = (Scale factor of length)³
Therefore;
Doubling the dimensions means that the volume of he room will be
multiplied by 2³ = 8 rather doubling the initial volume.
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