The volume of the pyramid is [tex]16\sqrt{3}[/tex] cm³ ⇒ 2nd answer
Step-by-step explanation:
The volume of a pyramid = [tex]\frac{1}{3}[/tex] base area × its height
The given is:
1. The base of the pyramid is an equilateral triangle of side length
[tex]4\sqrt{3}[/tex] cm
2. The area of the base is [tex]12\sqrt{3}[/tex] cm²
3. In Δ ACB measure of angle ACB is 90° and m∠ CAB is 30°
To find the volume of the pyramid we need its height
∵ The height of the pyramid is BC
- Because it is perpendicular to the side AC which is one side of the
base of the pyramid
∵ m∠CAB = 30°
∵ AC = [tex]4\sqrt{3}[/tex] cm
- By using tan(30) = [tex]\frac{BC}{AC}[/tex] we can find BC
∴ tan(30) = [tex]\frac{BC}{4\sqrt{3}}[/tex]
- By using cross multiplication
∴ BC = [tex]4\sqrt{3}*tan(30)[/tex]
∴ BC = 4 cm
∵ V = [tex]\frac{1}{3}[/tex] area of the base × BC
∵ BC = 4 cm
∵ The area of the base is [tex]12\sqrt{3}[/tex]
∴ V = [tex]\frac{1}{3}[/tex] × [tex]12\sqrt{3}[/tex] × 4
∴ V = [tex]16\sqrt{3}[/tex] cm³
The volume of the pyramid is [tex]16\sqrt{3}[/tex] cm³
Learn more:
You can learn more about volume of solids in brainly.com/question/12497249
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