A right circular cylinder having diameter 21, | vedclass

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Question

(A) Volume of the cylinder $= \pi R^2 H = \pi 	imes (10.5)^2 	imes 38 = \pi 	imes 110.25 	imes 38 = 4189.5\pi\, cm^3$.Volume of one ice cream cone

Vedclass · Accepted Answer

$54$

Vedclass · Answer

(A) Volume of the cylinder $= \pi R^2 H = \pi 	imes (10.5)^2 	imes 38 = \pi 	imes 110.25 	imes 38 = 4189.5\pi\, cm^3$.Volume of one ice cream cone (cone + hemisphere) $= \frac{1}{3}\pi r^2 h + \frac{2}{3}\pi r^3$.Given $r = 3.5\, cm$ and $h = 12\, cm$.Volume $= \frac{1}{3}\pi (3.5)^2 (12) + \frac{2}{3}\pi (3.5)^3 = \pi (12.25 	imes 4) + \pi (2 	imes 14.2916) \approx 49\pi + 28.583\pi = 77.583\pi\, cm^3$.Alternatively,using fractions: Volume $= \frac{1}{3}\pi (\frac{7}{2})^2 (12) + \frac{2}{3}\pi (\frac{7}{2})^3 = \pi (49) + \pi (\frac{343}{12}) = \pi (\frac{588+343}{12}) = \frac{931}{12}\pi\, cm^3$.Number of cones $= \frac{	ext{Volume of cylinder}}{	ext{Volume of one cone}} = \frac{4189.5\pi}{931\pi / 12} = \frac{4189.5 	imes 12}{931} = \frac{50274}{931} = 54$.

$A$ right circular cylinder having diameter $21\, cm$ and height $38\, cm$ is full of ice cream. The ice cream is to be filled in cones of height $12\, cm$ and diameter $7\, cm$ having a hemispherical shape on the top. The number of such cones to be filled with ice cream is

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