The height of a cone is twice the radius of its base. What expression represents the volume of the cone, in

cubic units?

23x3

49X3

2/3πx³

Step-by-step explanation:

Volume of a cone is expressed as;

V = 1/3πx²h ... 1

x is the radius

h is the height of the cone

If the height of a cone is twice the radius of its base, then;

h = 2x ... 2

Substitute equation 2 into 1

Recall that V =  1/3πx²h

V = 1/3πx²(2x)

V = 2/3πx³

Hence the expression that represents the volume of the cone is 2/3πx³ cubic units

answer:   the paragraph proof is mentioned below.

step-by-step explanation:

given: in a δxwy where

such that, ∠wzx ≅ ∠yzx and zw≅zy

we have to prove that: segment zx is a perpendicular bisector of segment wy.

prove: since, zw≅zy ⇒ ∠wzy is a supplementary angle.

then, ∠wzy= 180°

⇒∠wzx + ∠yzx = 180° ( because xz divides ∠wzy into two parts)

but, ∠wzx ≅ ∠yzx ( given)

⇒∠wzy+∠wzy=180° ( by substitution)

⇒2∠wzy=180°

⇒∠wzy=90°

⇒∠wzy=∠yzx =90°

therefore, xz⊥wy where wz=zy

⇒zx is a perpendicular bisector of wy.