The checker pieces are in the shape of a cylinder. They have a diameter of 2 feet and a height of
of a foot (8 inches). There are a total of 24 checker pieces. If the checker board has a volume of 35
cubic feet will the box have enough volume for the 24 checker pieces?
SHOW and EXPLAIN your work.

No

Step-by-step explanation:

Volume of one piece= πr^2h

=π ×1×1×1

=3.141

Volume of all the pieces=3.141×24

=75.38ft^3

Volume of board - volume of the pieces= 35-75.38

=-40.38

The answer is negative so the board doesn't have enough volume for all the pieces

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.