Respuesta :
To calculate for the total volume of the figure above, we add the separate volume of the cylinder and the cone. The volume of a cone is calculated from the product of the area of the circle times its height. The volume of the cone is calculated by 1/3 the product of the area of the base times the height.
V = Vcylinder + Vcone
V = πr²h + πr²h/3
V = π(6)²11 + π(6)²9/3
V = 1583.4 in^3 -------> closest to third option
V = Vcylinder + Vcone
V = πr²h + πr²h/3
V = π(6)²11 + π(6)²9/3
V = 1583.4 in^3 -------> closest to third option
The total volume of the composite figure is the sum of volume of cone and volume of cylinder
The volume of the composite figure shown in the image is 1583.4 cubed inches (rounded to nearest tenth).
How to find the volume of the composite figures?
To find volume of the composite figures,
- Separate the figure.
- Calculate the volume of the each figure by which the composite figure is made of.
- Add the volume of all the individual figures to get the total volume of composite figures.
Given information-
In the given figure the composite figure is made of one cone and one cylinder.
The height of the cylinder is 11 inches.
The radius of the cone and cylinder is 12 inches.
- A) Volume of the cylinder-
Volume of the cylinder can be find out using the below formula,
[tex]V=\pi r^2h[/tex]
Here [tex]r[/tex] is radius of the cylinder and [tex]h[/tex] is the height of the cylinder.
As The height of the cylinder is 11 inches and radius of the cylinder is 12 inches.
Thus find the volume by plug in the values in above formula as,
[tex]V=3.14 (6)^2\times11\\V=3.14 \times36\times11\\V=1243.44\rm in^3[/tex]
Hence the volume of the cylinder is 1243.44 cubed inches.
- B) Volume of the cone-
Volume of the cone can be find out using the below formula,
[tex]V=\dfrac{1}{3}\pi r^2h[/tex]
Here [tex]r[/tex] is radius of the cone and [tex]h[/tex] is the height of the cone.
The radius of the cone is 12 inches.
The height of the cone is the difference of total height to the cylinder height. Thus height of the cone is ,
[tex]h=20-11\\h=9\rm in[/tex]
Thus find the volume by plug in the values in above formula as,
[tex]V=\dfrac{1}{3}\times 3.14 (6)^2\times9\\V=\dfrac{1}{3}\times 3.14 \times36\times9\\V=339.12\rm in^3[/tex]
Hence the volume of the cone is 339.12 cubed inches.
The total volume of the composite figure is the sum of volume of cone and volume of cylinder thus,
[tex]V=339.12+1243.44\\V=1583.4\rm in^3[/tex]
Hence the volume of the composite figure shown in the image is 1583.4 cubed inches (rounded to nearest tenth).
Learn more about the volume of composite figures here;
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