Which pairs of angles in the figure below are vertical angles? Check all that apply.

A. SOB and AOB
B. SOE and DOA
C. BOA and BOE
D. EOA and DOS

The correct options are B and D:

B) SOE and DOA

D) EOA and DOS

Step-by-step explanation:

Vertical angles can be defined as those angles which are formed opposite to each other when two line are crossed. These angle have a common vertex. Vertical angles are always equal to each other.

Considering option A, <SOB and <AOB are not vertical angles as they are not opposite to each other.

Considering option B, <SOE and <DOA are vertical angles as they are opposite to each other.

Considering option C, <BOA and <BOE are not vertical angles as they are not opposite to each other.

Considering option D, <EOA and <DOS are vertical angles as they are opposite to each other.

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.