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Jet001 [13]
2 years ago
10

Find the volume for the regular pyramid. V =

Mathematics
2 answers:
dem82 [27]2 years ago
8 0

Answer:

16\sqrt{2}\\3

kakasveta [241]2 years ago
6 0

Answer:

Volume=\frac{16\sqrt{2} }{3}units^{3}

Step-by-step explanation:

∵ The volume of the pyramid = 1/3 base area  × height

∵ The base is equilateral Δ with side length 4

∴ The area of the bast = 1/4 × 4² × √3 = 4√3 units²

To get the height of the pyramid draw it from the vertex of the top of the pyramid ⊥ to the base on the centro-id of the base which divides the height of the triangle two ratio 2:1 from the vertex of the triangle

∵ The height of the base = √(4² - 2²) =√12 = 2√3

∴ 2/3 the height = 4√3/3 ⇒ (2:1 means 2/3 from the height)

∴ The height of the pyramid = √[4² - (4√3/3)²] = √[16 - 48/9]

∴ h = 4√2/√3 (4√6/3 in its simplest form)

∴ V = 1/3 × 4√3 × 4√2/√3 = 16√2/3 units³

∴ V = \frac{16\sqrt{2} }{3}

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