Question

Given a 10 foot length of tree trunk with a radius of 3 feet, what is the weight of the tree trunk section if it has a density of 45 lb/ft3? (to the nearest whole integer)

Answer 1

The answer is 12,723 lb

Use the formula for the volume of a cylinder to model the volume of the tree trunk.

V = πr^2h
V = π(3^2)(10)
V = 90π ft^3

therefore,

90π ft^3 × 45 lb/ft^3 = 12723.4502

Answer 2

Using the formula:

`\text{Weight} = \text{Density} * \text{Volume}`

As per the statement:

Given a 10 foot length of tree trunk with a radius of 3 feet.

Volume of tree trunk(V) is given by:

`V = \pi r^2h`

where, r is the radius and h is the length of the tree trunk.

Substitute r = 3 ft and h = 10 ft and use
`\pi = 3.14`

then;

`V = 3.14 \cdot 3^2 \cdot 10 = 282.6 ft^3`

It is also given it has a density of 45 lb/ft^3

then;

`\text{Weight} = 45 \cdot 282.6 = 12717 Ib`

Therefore, the the weight of the tree trunk section is, 12,717 Ib