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Svet_ta [14]
4 years ago
9

If a sphere’s volume is doubled, what is the corresponding change in its radius?

Mathematics
1 answer:
velikii [3]4 years ago
4 0
           Volume of a sphere = (4/3) (pi) (radius)³

The sphere's volume is proportional to the cube of its radius,
so the radius is proportional to the cube-root of the volume.

The only way to double a sphere's volume is to increase
its radius by the factor of
                                              ∛2 = 1.26 (rounded).
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The fencing of the left border costs $4 per foot, while the fencing of the lower border costs $1 per foot. (no fencing is requir
lord [1]
<span><u>Answer </u>
Left border = 8 feet
Lower border =32 feet
Area=128 〖ft〗^2


<u>Explanation </u>
The area is a right triangle.
Let us take the left border to be y feet and the lower border to be x feet
Area=1/2 yx
The cost of fencing would be 4y+x=64.
From this expression x=64-4y
Substituting this value of x in the area we have;
Area=1/2 y(64-4y)
A=32y-2y^2
To get the maximum area of the triangle the first derivative of the area would te equal to zero.
A=32y-2y^2
dA/dy=32-4y=0
4y=32
y=8
Since x=64-4y
x=64-(4×8)=32
The dimensions of the garden are 8 feet by 32 feet.
Since the garden is a right triangle,
Area=1/2×8×32
Area=128 〖ft〗^2 
</span>
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