Geometry Area, Volume and Dissection Arguments Quiz: 10 Questions with Explanations

A 10 piB 100 piC 4 piD 20 pi

V = pi x 2 squared x 5 = 20 pi. Using the diameter would give 100 pi.

A 45B 30C 270D 60

The cone is one third: 90 / 3 = 30.

A 36 piB 12 piC 9 piD 108 pi

(4/3) pi (27) = 36 pi. The value 108 pi forgets the 1/3.

A 144 piB 12 piC 72 piD 36 pi

The radius is 6, so the area is 36 pi. Using 12 as the radius gives 144 pi.

A The straight stack has more volumeB They have the same volumeC The slanted stack has more volumeD The volumes cannot be compared

Cavalieri’s principle: equal heights and equal cross-sectional areas mean equal volumes.

A 180B 60C 30D 90

V = (1/3)(36)(5) = 60. The value 180 is the prism volume.

A Becomes 4 times as largeB DoublesC Becomes 8 times as largeD Stays the same

V depends on r squared, so doubling r multiplies V by 4.

A 3B 2C 4D 6

A cube can be cut into three congruent pyramids, so each pyramid is one third of the cube.

A 36 piB 9 piC 18 piD 54 pi

Half of the sphere: 36 pi / 2 = 18 pi.

A 8B 2C 4D 34

The height is the square root of 25 – 9 = 4.