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Snezhnost [94]
3 years ago
10

Ariel is filling a giant beach ball with air. The radius of the beach ball is 30 cm. What is the volume of air that the beach ba

ll will hold?
Mathematics
2 answers:
boyakko [2]3 years ago
5 0
The answer is v=113040
Paraphin [41]3 years ago
4 0

Answer:

Volume of air that beach ball holds is 113040 cm³ .

Step-by-step explanation:

Formula

Volume\ of\ sphere = \frac{4}{3}\pi r^{3}

Where r is the radius of the sphere.

As given

Ariel is filling a giant beach ball with air.

The radius of the beach ball is 30 cm.

(As the shape of the beach ball in the shape of sphere .)

r = 30 cm

\pi = 3.14

Putting all the values in the formula

Volume\ of\ air\ that\ beach\ ball\ holds = \frac{4}{3}\times 3.14\times 30\times 30\times 30

Volume\ of\ air\ that\ beach\ ball\ holds= \frac{4\times 3.14\times 30\times 30\times 30}{3}

Volume\ of\ air\ that\ beach\ ball\ holds = \frac{339120}{3}

Volume of air that beach ball holds = 113040 cm³

Therefore the volume of air that beach ball holds is 113040 cm³ .


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The correct option is (b) h=0.5cos(\pi/6t)+9.5.

The equations can be used to model the height as a function of time, t, in hours is h=0.5cos(\pi/6t)+9.5.

<h3>Equation of cosine function:</h3>

The following is a presentation of the cosine function's generic form;

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Calculation for the model height;

The height, h (feet) of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet.

Obtain amplitude 'a' as

\begin{aligned}a &=\frac{\text { Maximum value }-\text { Minimum value }}{2} \\a &=\frac{10-9}{2} \\a &=\frac{1}{2} \\a &=0.5\end{aligned}

The time 'T' is calculated as-

\begin{aligned}&\mathrm{T}=\frac{2 \pi}{\mathrm{b}} \\&12=\frac{2 \pi}{\mathrm{b}} \\&\mathrm{b}=\frac{2 \pi}{12} \\&\mathrm{~b}=\frac{\pi}{6}\end{aligned}

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\begin{aligned}&\mathrm{d}=\frac{\text { Maximum value }+\text { Minimum value }}{2} \\&\mathrm{~d}=\frac{10+9}{2} \\&\mathrm{~d}=\frac{19}{2} \\&\mathrm{~d}=9.5\end{aligned}

Therefore, with the height as a function of time, t, expressed in hours, can be modeled by the following equations:

h=0.5cos(\pi/6t)+9.5

To know more about the general equation of a cosine function, here

brainly.com/question/27587720

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The complete question is-

The height, h, in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet. Which of the following equations can be used to model the height as a function of time, t, in hours? Assume that the time at t = 0 is 12:00 a.m.

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B. h=0.5cos(\pi/6t)+9.5

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