Is there more wood in a 70-foot-high tree trunk with a radius of 2.1 feet or in a 60-foot-high tree trunk with a radius of 2.4 feet? assume that the trees can be regarded as right circular cylinders.

there is
nothing
▼
ft
ft cubed
ft squared
of wood in the 70-foot-high tree and
nothing
▼
ft cubed
ft squared
ft
of wood in the 60-foot-high tree. there is more wood in the
▼
60
70
-foot-high tree

There is more wood in a 60-foot-high tree trunk with a radius of 2.4 feet

Step-by-step explanation:

* Lets talk about the right circular cylinder

- It has two circular bases

- The volume of it = Area of the base × its height

- The area of the base = πr²

- The quantity of wood in the tree is the volume of the cylinder

* Lets calculate the volumes the two trees and compare

 between them

- Volume of the first tree:

∵ Its radius = 2.1 feet

∴ The area of its base = π(2.1)² = 4.41π feet²

∵ Its height = 70 feet

∴ Its volume = 4.41π × 70 = 308.7π = 969.8 feet³

- Volume of the second tree:

∵ Its radius = 2.4 feet

∴ The area of its base = π(2.4)² = 5.76π feet²

∵ Its height = 60 feet

∴ Its volume = 5.76π × 60 = 345.6π = 1085.7 feet³

∵ 1085.7 > 969.8

∴ The volume of wood in 2nd tree > the volume of wood in 1st tree

* There is more wood in a 60-foot-high tree trunk with a radius of 2.4 feet

14 ft 7 inches

step-by-step explanation:

since each model inch corresponds to 25 real inches, 7 model inches will correspond to

7×25" = 175"

at 12" per foot, that is 14 feet, 7 inches.

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560