Question

Unit 11: volume & surface area homework 8

Answer 1

The volumes of the pyramids are listed below:

1. V = 1437.333 cm³
2. V = 75,398 km³
3. V = 59.2 ft³
4. V = 393.3 yd³
5. V = 1134.116 m³
6. V = 403.333 mm³
7. V = 405.6 in³
8. V = 886.808 ft³

How to determine the volume of a pyramid

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

Volume of the pyramid

V = (π/3) · B · h     (1)

Base of the pyramid - Circle

B = (π/4) · R²     (2)

Base of the pyramid - Regular polygon

B = (n · L²)/(4 · tan 0.5α)     (3)

Base of the pyramid - Right triangle

B = (1/2) · b · z     (4)

Base of the pyramid - Rectangle

B = b · z

Where:

• R - Radius
• n - Number of sides of the polygon.
• l - Side length
• α - Internal angle, in degree.
• h - 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) Square, n = 4, α = 90°, L = 14 cm, h = 22 cm

B = 196 cm², V = 1437.333 cm³

2) Circle, R = 3 km, h = 8 km

B ≈ 28.274 km², V = 75,398 km³

3) Right triangle, b = 12 ft, z = 3.7 ft, h = 8 ft

B = 22.2 ft², V = 59.2 ft³

4) Rectangle, b = 23 yd, z = 9 yd, h = 5.7 yd

B = 207 yd², V = 393.3 yd³

5) Circle, R = 9.5 m, h = 12 m

B ≈ 283.529 m², V = 1134.116 m³

6) Regular pentagon, B = 110 mm², h = 11 mm

V = 403.333 mm³

7) Square,n = 4, α = 90°, L = 13 in, h = 7.2 in

B = 169 in², V = 405.6 in³

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

B ≈ 110.851 ft², V = 886.808 ft³

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