Assume that a drop of water is spherical and | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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}

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(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:

Similar Questions

The radius of a cylinder is doubled and the height is halved. What is the ratio between the new volume and the previous volume?

The volume of a solid hemisphere is $19404 \, cm^3$. Its total surface area is ....... $cm^2$.

Find out the cost of the log of wood measuring $15 \frac{1}{2} \text{ m}$ by $2 \frac{3}{4} \text{ m}$ by $1 \frac{1}{3} \text{ m}$ at ₹ $45$ per $\text{cm}^3$ (in ₹).

$A$ rectangular tank is $30\,m$ long and $20\,m$ broad. Water is being flown into it through a square pipe of side $5\,cm$. What is the speed of water if the level of water in the tank rises by $1\,m$ in $8\,hours$? (in $km/h$)

$A$ ball of lead,$4\, cm$ in diameter,is covered with gold. If the volume of the gold and lead are equal,then the thickness of gold is approximately (in $cm$).
$[$ Given $\sqrt[3]{2} = 1.259 ]$

Vedclass Test Series

Exam Paper Generator

Online Exam Module