A cone whose height is 15 cm and radius of base is 6 cm, is trimmed sufficiently to reduce it to a pyramid whose base is an equilateral triangle. The volume of the portion of removed is
325cm3
328cm3
320cm3
332cm3
A
320cm3
B
325cm3
C
332cm3
D
328cm3
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Solution
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Height of a cone (h)=15cm
Radius of a cone (r)=6cm
⇒ Volume of a cone =13πr2h
=13×227×(6)2×15
=39607
=565.71cm3
Pyramid is an equilateral triangle of side 6√3cm
⇒ Area of equilateral triangle =√34×(side)2
=√34×(6√3)2
=27√3cm2
⇒ Volume of a pyramid of height 15cm=13×27√3×15
=135√3cm3
=233.82cm3
⇒ Difference between volume of cone and volume of pyramid =(565.71−233.82)cm3
=331.89cm3
=332cm3
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