A container shaped like a right circular cyli | vedclass

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(A) Height $(h_1)$ of the cylindrical container $= 15 \, cm$.Radius $(r_1)$ of the cylindrical container $= \frac{12}{2} = 6 \, cm$.Volume of the cyli

Vedclass · Accepted Answer

$10$

Vedclass · Answer

(A) Height $(h_1)$ of the cylindrical container $= 15 \, cm$.Radius $(r_1)$ of the cylindrical container $= \frac{12}{2} = 6 \, cm$.Volume of the cylindrical container $= \pi r_1^2 h_1 = \pi 	imes (6)^2 	imes 15 = 540\pi \, cm^3$.For the ice-cream cone,radius $(r_2) = \frac{6}{2} = 3 \, cm$ and height $(h_2) = 12 \, cm$.The cone has a hemispherical top with the same radius $r_2 = 3 \, cm$.Volume of one ice-cream cone $= 	ext{Volume of cone} + 	ext{Volume of hemisphere} = \frac{1}{3} \pi r_2^2 h_2 + \frac{2}{3} \pi r_2^3$.Volume of one ice-cream cone $= \frac{1}{3} \pi (3)^2 (12) + \frac{2}{3} \pi (3)^3 = 36\pi + 18\pi = 54\pi \, cm^3$.Let $n$ be the number of cones that can be filled.$n = \frac{	ext{Volume of cylinder}}{	ext{Volume of one ice-cream cone}} = \frac{540\pi}{54\pi} = 10$.Therefore,$10$ ice-cream cones can be filled.

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