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alexgriva [62]
2 years ago
5

Unit 11: volume & surface area homework 8

Mathematics
1 answer:
Sholpan [36]2 years ago
7 0

The volumes of the pyramids are listed below:

  1. <em>V =</em> 1437.333 cm³
  2. <em>V =</em> 75,398 km³
  3. <em>V =</em> 59.2 ft³
  4. <em>V =</em> 393.3 yd³
  5. <em>V =</em> 1134.116 m³
  6. <em>V =</em> 403.333 mm³
  7. <em>V =</em> 405.6 in³
  8. <em>V =</em> 886.808 ft³
<h3>How to determine the volume of a pyramid</h3>

Volume is the space occuppied by an object. In this question we must determine the volumes of pyramids of <em>circular</em> <em>base</em> and <em>polygonal</em> base (<em>V</em>). All the formulas needed are described below:

<h3>Volume of the pyramid</h3>

<em>V = (</em>π<em>/</em>3<em>) · B · h</em>     (1)

<h3>Base of the pyramid - Circle</h3>

<em>B = (</em>π<em>/</em>4<em>) · R²</em>     (2)

<h3>Base of the pyramid - Regular polygon</h3>

<em>B = (n · L²)/(</em>4 <em>· tan </em>0.5α<em>)</em>     (3)

<h3>Base of the pyramid - Right triangle</h3>

<em>B = (</em>1/2<em>) · b · z</em>     (4)

<h3>Base of the pyramid - Rectangle</h3>

<em>B = b · z</em>

Where:

  • <em>R</em> - Radius
  • <em>n</em> - Number of sides of the polygon.
  • <em>l</em> - Side length
  • <em>α</em> - Internal angle, in degree.
  • <em>h</em> - Height of the pyramid
  • b - Base of the right triangle/rectangle.
  • z - Length of the right triangle/rectangle.

Now we proceed to solve each pyramid:

1) <em>Square</em>, <em>n =</em> 4, <em>α =</em> 90°, <em>L =</em> 14 cm, <em>h =</em> 22 cm

<em>B =</em> 196 cm², <em>V =</em> 1437.333 cm³

2) <em>Circle</em>, <em>R =</em> 3 km, <em>h =</em> 8 km

<em>B ≈</em> 28.274 km², <em>V =</em> 75,398 km³

3) <em>Right triangle</em>, <em>b =</em> 12 ft, <em>z =</em> 3.7 ft, <em>h =</em> 8 ft

<em>B =</em> 22.2 ft², <em>V =</em> 59.2 ft³

4) <em>Rectangle</em>, <em>b =</em> 23 yd, <em>z =</em> 9 yd, <em>h =</em> 5.7 yd

<em>B =</em> 207 yd², <em>V =</em> 393.3 yd³

5) <em>Circle</em>, <em>R =</em> 9.5 m, <em>h =</em> 12 m

<em>B ≈</em> 283.529 m², <em>V =</em> 1134.116 m³

6) <em>Regular pentagon</em>, <em>B =</em> 110 mm², <em>h =</em> 11 mm

<em>V =</em> 403.333 mm³

7) <em>Square</em>,<em>n =</em> 4, <em>α =</em> 90°, <em>L =</em> 13 in, <em>h =</em> 7.2 in

<em>B =</em> 169 in², <em>V =</em> 405.6 in³

8) <em>Regular triangle</em>, <em>n =</em> 3, <em>α =</em> 120°, <em>L =</em> 16 ft, <em>h =</em> 24 ft

<em>B ≈</em> 110.851 ft², <em>V =</em> 886.808 ft³

To learn more on volumes, we kindly invite to check this verified question: brainly.com/question/1578538

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