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Gala2k [10]
3 years ago
7

Determine, to one decimal place, the length, width & height of the rectangular prism that would have the greatest volume, wi

th a surface area of 200 cm^2.
Mathematics
1 answer:
Leya [2.2K]3 years ago
7 0

Answer:

The length = The width = The height  ≈ 5.8 cm

Step-by-step explanation:

The volume of a rectangular pyramid, V = l × w × h

The surface area of the pyramid = 2 × l × h + 2 × w × h + 2 × l × w = 200

∴  l × h + w × h + l × w = 200/2 = 100

We have that the maximum volume is given when the length, width, and height are equal and one length is not a fraction of the other. Therefore, we get;

At maximum volume, l = w = h

∴ l × h + w × h + l × w = 3·l² = 100

l² = 100/3

l = 10/√3

Therefore, the volume, v = l³ = (10/√3)³

The length = The width = The height = 10/√3 cm ≈ 5.8 cm

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3 years ago
Locate 81/5,8.5,84/5,8.44 on a number line then write the numbers in order from least to greatest
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3 years ago
Two identical number cubes are shown in the picture below. The edge length of these number cubes is 4 centimeters: What is the c
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d. 128 cm^3

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12. 5

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2 years ago
if log 2 = ( 0.3010 ), Log 3 = ( 0.4771 ) and Log 5 = ( 0.6990 ) then find the value of the following: Log 24... The answer is (
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