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From a solid right circular cylinder with height 10 cm and radius of the base 6 cm, a right circular cone of the same height and base is removed. The volume of the remaining solid is ____.

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Detailed Solution

From a solid right circular cylinder with height 10 cm and radius of the base 6 cm, a right circular cone of the same height and base is removed. The volume of the remaining solid is 754

c m^{3}

.
Given, right circular cylinder with height 10 cm and radius of the base 6 cm.
We know that, volume of a cone =

\frac{1}{3}

times of volume of cylinder.
If the cone is removed from the cylinder then the remaining volume = cylinder volume-cone volume .
= cylinder volume -

\frac{1}{3}

(cylinder volume)
=

\frac{2}{3}

(cylinder volume)
Volume of the remaining portion =

\frac{2}{3} π r^{2} h

= \frac{2}{3} π {(6)}^{2} 10

= 754 c m^{3}

So, the volume of remaining portion is

754 c m^{3}

.
Hence, the correct answer is 754

c m^{3}

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