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Masja [62]
4 years ago
5

The diameter of Z is 5 in. What is its area in terms of pi?

Mathematics
2 answers:
irina [24]4 years ago
6 0
We are given the diameter of the circle, I assume. In this case, the formula of the area of the circle is expressed as A = pi d^2/4. where pi is a constant. The only option taht makes sense here is C. 6.25 in2. This should have the constant pi on it. 
vaieri [72.5K]4 years ago
4 0

we know that

the area of the circle is equal to

A=\pi r^{2}

where

r is the radius of the circle

In this problem we have

Diameter=5\ in\\r=Diameter/2\\r=5/2\\r=2.5\ in

substitute the value of r in the area's formula

A=\pi*2.5^{2}

A=6.25\pi\ in^{2}

therefore

<u>the answer is</u>

6.25\pi\ in^{2}

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The length of the brace required is 4.3m

What is sine rule?

In a ΔABC a, b and c are the sides and A, B and C are angles then,

\frac{a}{SinA}=\frac{b}{sinB}=\frac{c}{sinC}

We can find the length, l as shown below:

Let AB=3m, BC=2m and AC=l

Let ∠A=25°

So, in ΔABC

\frac{BC}{sinA}=\frac{AB}{sinC}=\frac{AC}{SinB}

\frac{BC}{sinA}=\frac{AB}{sinC}

\frac{2}{sin25}=\frac{3}{sinC}

\angle{C}=sin^{-1}(\frac{3\times sin25}{2} )

∠C=39.34°

∠A+∠B+∠C=180°

∠B=180°-25°-39.34°

∠B=115.66°

\frac{BC}{sinA}=\frac{AC}{SinB}

\frac{2}{sin25}=\frac{l}{sin(115.66)}

l=\frac{2\times sin(115.66)}{sin25}

l=4.2659

Rounding to nearest tenth of meter.

l=4.3m

Hence, the length of the brace required is 4.3m

Learn more about Sine Rule here:

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