Assume that a drop of water is spherical and | vedclass

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(D) Let the height of the conical glass be $h 	ext{ cm}$.Since the height is equal to the diameter of the rim,the radius of the rim $r = \frac{h}{2}

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$4$

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(D) Let the height of the conical glass be $h 	ext{ cm}$.Since the height is equal to the diameter of the rim,the radius of the rim $r = \frac{h}{2} 	ext{ cm}$.The volume of the conical glass is given by $V_{	ext{glass}} = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi (\frac{h}{2})^2 h = \frac{\pi h^3}{12}$.The diameter of a spherical water drop is $\frac{1}{10} 	ext{ cm}$,so its radius $r_d = \frac{1}{20} 	ext{ cm}$.The volume of one drop is $V_{	ext{drop}} = \frac{4}{3} \pi r_d^3 = \frac{4}{3} \pi (\frac{1}{20})^3 = \frac{4 \pi}{3 	imes 8000} = \frac{\pi}{6000} 	ext{ cm}^3$.Given that $32,000$ drops fill the glass,$V_{	ext{glass}} = 32000 	imes V_{	ext{drop}}$.$\frac{\pi h^3}{12} = 32000 	imes \frac{\pi}{6000}$.$\frac{h^3}{12} = \frac{32}{6} = \frac{16}{3}$.$h^3 = \frac{16}{3} 	imes 12 = 16 	imes 4 = 64$.$h = \sqrt[3]{64} = 4 	ext{ cm}$.

Assume that a drop of water is spherical and its diameter is $\frac{1}{10} \text{ cm}$. $A$ conical glass has a height equal to the diameter of its rim. If $32,000$ drops of water fill the glass completely,then the height of the glass (in $\text{cm}$) is:

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