Question

What is the volume of the geometric solid produced by the triangle below

Answer 1

Answer:

The volume of the geometric solid produced is 391 cubic cm ⇒ A

Step-by-step explanation:

When a right triangle is rotated about its vertical leg 360°, then it formed a cone its radius is the horizontal leg of the triangle and its height is the vertical lege of the triangle.

The rule of the volume of the cone is V = $\frac{1}{3}$ π r² h, where

• r is the radius of its base

• h is the length of its height

∵ Triangle XYZ is rotated 360° about the vertical side YZ

∴ It formed a cone with a radius = XZ and a height = YZ

∵ $\frac{YZ}{XZ}=tan(60)$

∵ YX = 6√3

∴ $\frac{6\sqrt{3}}{XZ}=tan(60)$

∵ tan(60) = √3

∴ $\frac{6\sqrt{3}}{XZ}$ = √3

→ By using cross multiplication

∴ 6√3 = XZ(√3)

→ Divide both sides by √3

∴ 6 = XZ

∵ XZ = r and YZ = h

∴ r = 6 and h = 6√3

→ By using the rule of the cone above

∵ V = $\frac{1}{3}$ (π) (6)² (6√3)

∴ V ≅ 391 cm³

∴ The volume of the geometric solid produced is 391 cubic cm