Answered

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A cone-shaped hole is cut out of a cube. How much of the cube is left? Round your answer to the nearest cubic centimeter.

A Coneshaped Hole Is Cut Out Of A Cube How Much Of The Cube Is Left Round Your Answer To The Nearest Cubic Centimeter class=

Sagot :

Answer:

191

Explanation:

The volume left equals

Volume lefft = volume of the cube - the volume of the cone

Now

[tex]cube\; volume=6\operatorname{cm}\times6\operatorname{cm}\times6\operatorname{cm}=216\operatorname{cm}[/tex]

and

[tex]cone\; volume=\frac{\pi r^2h}{3}[/tex]

since r = 2 cm and h = 6 cm, we have

[tex]cone\; volume=\frac{\pi(2)^2\cdot6}{3}=8\pi\; cm^3[/tex]

Hence,

[tex]volume\; left=216\operatorname{cm}-8\pi cm^3[/tex][tex]volume\; left=190.867\operatorname{cm}^3[/tex]

rounded to the nearest cubic centimeter gives

[tex]\boxed{volume\; left=191\operatorname{cm}}[/tex]

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