Respuesta :
Complete question:
A cone is stacked on top of a cylinder. They both share a circular base. The total height of the composite figure is 25. The height of the cylinder is 13 and the radius is 5. Which expression represents the volume, in cubic units, of the composite figure?
A) Pi(5²)(13) – One-third pi (5²)(12)
B) Pi(5²)(13) – One-third pi (5²)(25)
C) Pi(5²)(13) + One-third pi (5²)(12)
D) Pi(5²)(13) + One-third pi (5²)(25)
Answer:
Pi(5²)(13) + One-third pi (5²)(12)
Step-by-step explanation:
Given:
Height of cylinder = 13
radius of cylinder = 5
Total height = 25
Since the cone and cylinder are stacked together, to find the height of cone, let's subtract the height of the cylinder from the total height.
Height of cone, h = 25 - 13 = 12
The cone and cylinder both share a circular base, which means they have the same radius.
Radius of cone, r= Radius of cylinder, r
To find the volume, we use:
Volume of cylinder + Volume of cone
Volume of cylinder is expressed as:
Pi(r²)h
Substiting figures, we have:
Pi(5²)13
Volume of cone is expressed as:
⅓pi(r²)h
Substiting figures, we have:
⅓pi(5²)12
Therefore, the expression that represents the volume is:
Pi(5²)13 + ⅓pi(5²)12
Correct option is option (C).
Pi(5²)(13) + One-third pi (5²)(12)
The total volume of the composite figure is [tex]\rm \dfrac{1}{3}\times \pi \times (12)+\pi\times (25) \times (13)[/tex] and this can be determined by using the formula of the volume of the cone and cylinder.
Given :
- A cone is stacked on top of a cylinder. They both share a circular base.
- Composite figure height is 25.
- Cylinder height is 13 and the radius is 5.
The following steps can be used in order to determine the expression that represents the volume, in cubic units, of the composite figure:
Step 1 - First, determine the volume of the cone.
[tex]\rm V' = \dfrac{1}{3}\times \pi \times r^2 \times h[/tex]
where 'r' is the radius and 'h' is the height of the cone.
Substitute the values of the known terms in the above expression.
[tex]\rm V' = \dfrac{1}{3}\times \pi \times (25) \times 12[/tex]
Step 2 - Now, determine the volume of the cylinder.
[tex]\rm V'' = \pi \times r^2 \times h[/tex]
where 'r' is the radius and 'h' is the height of the cylinder.
Substitute the values of the known terms in the above expression.
[tex]\rm V'' = \dfrac{1}{3}\times \pi \times (25) \times 13[/tex]
Step 3 - So, the total volume of the composite figure is:
[tex]\rm V = V'+V''[/tex]
[tex]\rm V = \dfrac{1}{3}\times \pi \times (12)+\pi\times (25) \times (13)[/tex]
Therefore, the correct option is C).
For more information, refer to the link given below:
https://brainly.com/question/1578538
