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A wooden box is in the shape of a regular pentagonal prism. The sides, top, and bottom of the box are 1 centimeter thick. Approximate the volume of wood used to construct the box. Round your answer to the nearest tenth. brainly

Sagot :

Answer:

Volume of regular pentagonal prism = 1.72 cm³ (Approx.)

Step-by-step explanation:

Given:

Side of regular pentagonal prism = 1 cm

Height of regular pentagonal prism = 1 cm

Find:

Volume of regular pentagonal prism

Computtaion:

Volume of regular pentagonal prism = (1/4)[√5(5+2√5)]a²h

Volume of regular pentagonal prism = (1/4)[√5(5+2√5)](1)²(1)

Volume of regular pentagonal prism = (1/4)[√5(5+2√5)]

Volume of regular pentagonal prism = (0.25)[√5{5+4.472}]

Volume of regular pentagonal prism = (0.25)[√5{9.472}]

Volume of regular pentagonal prism = (0.25)[√47.36]

Volume of regular pentagonal prism = (0.25)[6.8818]

Volume of regular pentagonal prism = 1.72045

Volume of regular pentagonal prism = 1.72 cm³ (Approx.)

yangjinrui9296

Answer:

217.96 or 218.0 in Big Ideas Math

  • Thanks Harlan for helping me understand this problem

Step-by-step explanation:

volume of the whole prism - smaller inner prism

Bigger Prism (apothem = 4, height = 6)

360/5 = 72   72/2 = 36

4 · tan (36) = 2.906

2.906 · 4 = 11.6247

11.6247 · 5 = 58.1234  ← The area of the Pentagon

58 · 6 = 348.740 ← The Bigger Prism Volume

Smaller Prism (apothem = 3, height = 4)

Keep in mind that the bottom, sides, and top of the box is one centemeters thick ⇒ smaller pentagon ⇒ (apothem = 4-1, height = 6 - 2)

3 · tan (36) = 2.1796

2.1796 · 3 = 6.5389

6.5389 · 5 = 32.6944  ← small Pentagon Area

32.6944 · 4 = 130.7777  ← Small Pentagon Prism Volume

Final Step

Area of big prism - small prism

348.74041 - 130.7777 = 217.9627

Round to the nearest tenth ⇒ 218.0

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