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The figure is made up of two cones and a cylinder. Both cones and the cylinder have a 10 mm diameter.

What is the exact volume of this figure?

What is the volume of this figure?


250π mm³

400π mm³

625π mm³

2500π mm³

The figure is made up of two cones and a cylinder Both cones and the cylinder have a 10 mm diameter What is the exact volume of this figure What is the volume o class=

Respuesta :

calculista

Answer:

[tex]625\pi\ mm^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the figure is equal to the volume of two cones plus the volume of the cylinder

Find the volume of one cone

[tex]V=\frac{1}{3}\pi r^{2} h[/tex]

we have

[tex]r=10/2=5\ mm[/tex] -----> the radius is half the diameter

[tex]h=15\ mm[/tex]

substitute the values

[tex]V=\frac{1}{3}\pi (5^{2})(15)=125\pi\ mm^{3}[/tex]

Find the volume of the cylinder

[tex]V=\pi r^{2} h[/tex]

we have

[tex]r=10/2=5\ mm[/tex] -----> the radius is half the diameter

[tex]h=15\ mm[/tex]

substitute the values

[tex]V=\pi (5^{2})(15)=375\pi\ mm^{3}[/tex]

Find the volume of the figure

[tex]2*125\pi\ mm^{3}+375\pi\ mm^{3}=625\pi\ mm^{3}[/tex]

JeanaShupp

Answer: 625π mm³

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Step-by-step explanation:

Volume of cone = [tex]\dfrac{1}{3}\pi r^2h[/tex] , where r is radius and h is height of cone.

Volume of cylinder = [tex]\pi R^2H[/tex], where R is radius and H is height of cone.

For given picture,

Diameter of cone and cylinder = 10 mm , then radius = 5 mm (half of diameter)

h= 15 mm , r= 5mm

R= 5mm ,  H=15mm

Combined volume of figure = 2 x (Volume of cone)+ Volume of cylinder

[tex]=2\times(\dfrac{1}{3}\pi (5)^2(15))+\pi (5)^2(15)\\\\=250\pi+375\pi\\\\=625\pi\ mm^3[/tex]

Hence, the volume of this figure is 625π mm³

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