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copelandgarret9972
28.01.2020 •
Mathematics
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
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Ответ:
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
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