Question

What prism or other 3-dimensional shape would you use to model the tree trunk below? (Rectangular prism, triangular prism, square prism, or cylinder). If the height of the tree trunk is 13 ft and the radius is 1.5 ft, what is the volume in cubic feet?

Answer 1

VOLUME OF A CYLINDER

Problem:

What prism or other 3-dimensional shape would you use to model the tree trunk below? (Rectangular prism, triangular prism, square prism, or cylinder). If the height of the tree trunk is 13 ft and the radius is 1.5 ft, what is the volume in cubic feet?

Answer:

• 
  `\color{hotpink} \bold{91.85 \: \: ft}`

— — — — — — — — — —

— I will use cylinder to model the tree trunk since it's looks like. (Please refer to the pic)

Formula:

• 
  `\underline{ \boxed{ \sf \: V=πr²h}}`

where,

• V is the Volume
• π (pi) is the constant 3.14
• r is the radius
• h is the height

– This formula is used when the radius of the base is given.

Solution:

Remember that radius has to be multiplied by itself (squared). And pi (π) is the constant 3.14.

– Using the formula above, substitute the givens in the formula then solve.

• 
  `V=πr²h`

• 
  `V=3.14 * (1.5)² * 13`

• 
  `V=3.14 * (2.25 * 13)`

• 
  `V= \underline{ \boxed{ \blue{ 91.85 \: ft ^(3) }}}`

Hence, the volume is 91.85 ft³.

_______________∞_______________

Answer 2

• cylinder
• 91.9 ft³

Explanation:

a)

An object with a uniform circular cross section is generally modeled by a cylinder.

__

b)

The formula for the volume of a cylinder is ...

V = πr²h

For the given radius and height, the volume is ...

V = π(1.5 ft)²(13 ft) ≈ 91.9 ft³

The volume of the tree trunk is about 91.9 ft³.