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expeople1 [14]
2 years ago
5

A sixth-grade science club needs $180 to pay for the tickets to a science museum. All tickets cost the same amount. What could "

180 / 15" (180 divided by 15) mean in this context? Describe two interpretations of the expression. Then, find the quotient (answer) and explain what it means in each interpretation.
Mathematics
1 answer:
ollegr [7]2 years ago
6 0

Answer:

12

Step-by-step explanation:

180 ÷ 15 = 12

15 can go into 180 , 12 times

15 x 12 = 180

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liq [111]

Check the picture below.

since the diameter of the cone is 6", then its radius is half that or 3", so getting the volume of only the cone, not the top.

1)

\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=4 \end{cases}\implies V=\cfrac{\pi (3)^2(4)}{3}\implies V=12\pi \implies V\approx 37.7

2)

now, the top of it, as you notice in the picture, is a semicircle, whose radius is the same as the cone's, 3.

\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=3 \end{cases}\implies V=\cfrac{4\pi (3)^3}{3}\implies V=36\pi \\\\\\ \stackrel{\textit{half of that for a semisphere}}{V=18\pi }\implies V\approx 56.55

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well, you'll be serving the cone and top combined, 12π + 18π = 30π or about 94.25 in³.

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pretty much the same thing, we get the volume of the cone and its top, add them up.

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