9514 1404 393
Answer:
7. 4 cm
8. 206 paper cups
9. 175pi cm³
Explanation:
7. The formula for the volume of a cone can be used.
V = 1/3πr²h
h = 3V/(πr²) = 3(48π cm³)/(π(6 cm)²) = 144/36 cm = 4 cm
The height of the cone is 4 cm.
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8. The volume of the cone with the given dimensions is ...
V = 1/3π(4 cm)²(11 cm) = 176/3π cm³ ≈ 184.307 cm³
The number of times this volume can be filled by 10 gallons is ...
(10 gal)(3785 cm³/gal)/(184.307 cm³/cup) = 205.3 cups
206 paper cups are needed.
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9. We know from the formula for the volume of a cone that it has the same volume as a cylinder 1/3 its height. The composite figure is equivalent to a cylinder with a height of ...
3 cm +(12 cm)/3 = 7 cm
Then the volume is ...
V = πr²h
V = π(5 cm)²(7 cm) = 175π cm³
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For this, we recognize that the triangle with sides h, 5, and 13 will be a 5-12-13 right triangle, so the height of the conical part of the figure is h=12 cm. If you haven't remembered that Pythagorean triple, you can find the height from the Pythagorean theorem:
h² +5² = 13²
h = √(169 -25) = √144 = 12