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professor190 [17]

2 years ago

5

A building engineer analyzes a concrete column with a circular cross section. The circumference of the column is 18pi meters. Wh

at is the area A of the cross section of the column?

2 answers:

ella [17]2 years ago

3 0

Answer

Circumference(C) of a circle is given by:

$C = 2\pi r$

where r is the radius and value of $\pi = 3.14$

As per the given statement:

A building engineer analyzes a concrete column with a circular cross section.

The circumference of the column is $18 \pi$ meters.

then;

$18 \pi= 2\pi r$

Divide both sides by $2 \pi$ we have;

9 = r

or

r = 9 meters

We have to find the area of the cross section of the column

Area of a circle is given by:

$A = \pi r^2$

then;

$A = \pi \cdot 9^2 = 81 \pi$ meter square.

therefore, the area A of the cross section of the column is $81 \pi$ meter square.

iren [92.7K]2 years ago

3 0

Check the picture below

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A rectangular piece of plywood has a diagonal which measures two feet more than the width. The length of the plywood is twice th

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The length of the plywood's diagonal(to the nearest tenth) is, 3.6 and 1.4

Step-by-step explanation:

let l be the length and w be the width of the rectangle respectively;

Diagonal(D) of a rectangle is given by:

$D = \sqrt{l^2+w^2}$ ......[1]

As per the given statement we have;

Diagonal(D) = width + 2

and

$l = 2 \times w$ = 2w

Now, substitute these in [1] we have;

$\sqrt{(2w)^2+w^2} = w+5$

Squaring both the sides we get;

$4w^2+w^2 = (w+2)^2$

$5w^2 = w^2 + 4 + 4w$

or

$5w^2 -w^2 = 4w + 4$ or

$4w^2= 4w + 4$

Simplify:

$w^2-w-1 =0$ ......[2]

The quadratic equation is in the form of $ax^2+bx+c = 0$

the solution is given by: $x = \frac{-b \pm\sqrt{b^2-4ac}}{2a}$

On comparing with [1] we get

a= 1 , b = -1 and c = -1

Then the solution is:

$w= \frac{-(-1) \pm\sqrt{(-1)^2-4(1)(-1)}}{2(1)}$

$w =\frac{1 \pm\sqrt{1+4}}{2} = \frac{1 \pm\sqrt{5}}{2}$

Simplify:

$w \approx 1.62$ and $w \approx -0.62$

Then, the diagonal D = w+2

For $w \approx 1.62$

$D = 1.62 +2 \approx 3.62$

For $w \approx -0.62$

$D =-0.62 +2 \approx 1.38$

therefore, the length of the plywood's diagonal(to the nearest tenth) is, 3.6 and 1.4

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2 years ago