Answer :
The volume of a mathematically similar paperweight with height 7 cm, the volume ratio (64:343) based on the cube of their heights (4 cm and 7 cm) is used. Multiplying the known volume (38.4 cm3) by this ratio gives the volume of the second paperweight as approximately 205.714 cm3.
The question is asking to calculate the volume of a mathematically similar paperweight with a height of 7 cm, knowing that another paperweight with a height of 4 cm has a volume of 38.4 cm3. When dealing with similar shapes, we use ratios. The ratio of the linear dimensions of two similar geometric objects is proportional to the cube root of the ratio of their volumes. Therefore, if the height of the first paperweight is to the height of the second as 4:7, the volumes will be as 43:73 or 64:343.
First, we find the volume ratio:
Volume ratio = (Height of paperweight 1)3 / (Height of paperweight 2)3
Volume ratio = 43 / 73 = 64/343
Next, we apply this ratio to find the second paperweight's volume:
Volume of paperweight 2 = Volume of paperweight 1 × (Volume ratio of paperweight 2 to paperweight 1)
Volume of paperweight 2 = 38.4 cm3 × (343/64)
Volume of paperweight 2 = 38.4 cm3 × 5.359375
Volume of paperweight 2 = 205.714 cm3
Therefore, the volume of the mathematically similar paperweight with a height of 7 cm is approximately 205.714 cm3.
The similar paperweight has a volume of 67.2 cubic cm if the height is 7 cm.
What is volume?
It is defined as a three-dimensional space enclosed by an object or thing.
As we know,
Volume = base area×height
38.4 = base area×4
base area = 38.4/4 = 9.6 square cm
A mathematically similar paperweight has a height of 7 cm.
Volume = base area×height
Volume = 9.6×7 = 67.2 cubic cm
Thus, the similar paperweight has a volume of 67.2 cubic cm if the height is 7 cm.
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