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lavishautumn
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A right triangle with vertices J(2, 0), K(0,0), and L(0,9) is rotated around the x-axis.

AUse complete sentences to describe the resulting solid. Include the specific measurements for the solid’s dimensions such as height, width, length, radius, etc. B. To the nearest tenth of a cubic unit, what is the volume of the resulting three-dimensional figure? Include all of your calculations.

Verified Answer :

apologiabiology

if we imagine it in our head, we can see that the width (base) is 2 and the height is 9
the area is 1/2bh or 1/2*2=9 square units
it is rotated around x axis
meaning we have a sideways cone that is 2 hight and radius is 9
Vcone=1/3(hpir^2)
h=2
r=9
V=(1/3)(2)(3.141592)(9^2)
V=(2/3)(3.141592)(81)
V=(54)(3.141592)
V=169.6459
round
V=169.6 cubic units




base is 2 units
height is 9 units
area is 9 square units
it's a cone (sideways)
it has a volume of 169.6 cubic units

Answer:

Volume of cone = 169.6 cubic unit

Step-by-step explanation:

In the given triangle height of the triangle is 9 unit and the base is 2 units.

Now this triangle is rotated around x-axis which forms a cone with circular base of radius = 9 unit and height of 2 units

Now volume of this cone formed will be

V = (1/3)π×r²×h

V = (1/3)(3.14)(9)²(2) = (1/3)(3.14)(162) = (3.14)(54) = 169.6 unit³

Therefore the resulting solid is a cone with a circular base of radius 9 units, height 2 units and volume 169.6 cubic unit.

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