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3 years ago

The area of a circle with a radius of 26 inches

Mathematics

2 answers:

brilliants [131]3 years ago

5 0

Answer:

the area of a circle with a radius of 26 inches (diameter of 52 inches) 2,123.7 square inches

Step-by-step explanation:

1. To find the area of a circle with the radius, square the radius, or multiply it by itself.

2. Then, multiply the squared radius by pi, or 3.14, to get the area.

3. To find the area with the diameter, simply divide the diameter by 2, plug it into the radius formula.

4. solve as before.

exis [7]3 years ago

4 0

Answer:

2,123.7 square inches

Step-by-step explanation:

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A farmer is constructing a rectangular pen with one additional fence across its width. Find the maximum area that can be enclose

konstantin123 [22]

The maximum area of the pen is the highest area the pen can have

The maximum area is 16200 square yards

Let the dimension be x and y.

So, the perimeter is given as:

$\mathbf{P = 360}$

Because it has one additional fence, the perimeter is calculated as:

$\mathbf{2x + y = 360}$

Make y the subject

$\mathbf{y = 360 - 2x}$

The area is calculated as:

$\mathbf{A = xy}$

Substitute $\mathbf{y = 360 - 2x}$

$\mathbf{A = x(360 -2x)}$

Expand

$\mathbf{A = 360x -2x^2}$

Differentiate

$\mathbf{A' = 360 -4x}$

Set to 0

$\mathbf{360 -4x = 0}$

Rewrite as:

$\mathbf{4x = 360}$

Divide both sides by 4

$\mathbf{x = 90}$

Substitute 90 for x in $\mathbf{A = 360x -2x^2}$

$\mathbf{A = 360 \times 90 - 2 \times 90^2}$

$\mathbf{A = 16200}$

Hence, the maximum area is 16200 square yards