Answered

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Inez carved a wooden cone from a
cylindrical piece of wood. The cylindrical
piece of wood had a radius of 3 inches
and a height of 15 inches. The cone had
the same radius as the cylinder but was
2 inches shorter. About what volume of
wood did Inez remove from the cylinder to
make the cone?

Inez Carved A Wooden Cone From A Cylindrical Piece Of Wood The Cylindrical Piece Of Wood Had A Radius Of 3 Inches And A Height Of 15 Inches The Cone Had The Sam class=

Sagot :

theleangreenbean

Answer:

123 inches³

Step-by-step explanation:

Hi there!

Objective: Find the volume of the cone

We know that the cylinder had a radius of 3 inches and it had a height of 15 inches.

Because the cone had the same radius of the cylinder, we know that it has a radius of 3 inches. And because it was 2 inches shorter, it has a height of 13 inches (15-2=13).

[tex]V=\frac{1}{3} \pi r^2h[/tex]  where r is the radius of the cone and h is its height

Plug in the known information (r=3 and h=13)

[tex]V=\frac{1}{3} \pi (3)^2(13)\\V=\frac{1}{3} \pi (9)(13)\\V=\frac{1}{3} \pi(117)\\V=39\pi\\V=123[/tex]

Therefore, the Inez removed about 123 inches³ of wood from the cylinder to make the cone.

I hope this helps!

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