A vessel is in the form of an inverted cone. | vedclass

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

Question

(A) Height $(h)$ of the conical vessel $= 8 \, cm$.Radius $(r_1)$ of the conical vessel $= 5 \, cm$.Radius $(r_2)$ of each lead shot $= 0.5 \, cm$.Let

Vedclass · Accepted Answer

$100$

Vedclass · Answer

(A) Height $(h)$ of the conical vessel $= 8 \, cm$.Radius $(r_1)$ of the conical vessel $= 5 \, cm$.Radius $(r_2)$ of each lead shot $= 0.5 \, cm$.Let $n$ be the number of lead shots dropped into the vessel.According to the problem,the volume of water that flows out is equal to the total volume of the lead shots dropped.Volume of water spilled $= \frac{1}{4} 	imes$ Volume of the cone.$\frac{1}{4} 	imes (\frac{1}{3} \pi r_1^2 h) = n 	imes (\frac{4}{3} \pi r_2^3)$.Canceling $\frac{1}{3} \pi$ from both sides:$\frac{1}{4} r_1^2 h = 4 n r_2^3$.$r_1^2 h = 16 n r_2^3$.Substituting the values:$5^2 	imes 8 = 16 	imes n 	imes (0.5)^3$.$25 	imes 8 = 16 	imes n 	imes (\frac{1}{2})^3$.$200 = 16 	imes n 	imes \frac{1}{8}$.$200 = 2n$.$n = 100$.Thus,the number of lead shots dropped in the vessel is $100$.

Similar Questions

In one fortnight of a given month,there was a rainfall of $10 \, cm$ in a river valley. If the area of the valley is $7280 \, km^2$,show that the total rainfall was approximately equivalent to the addition to the normal water of three rivers each $1072 \, km$ long,$75 \, m$ wide,and $3 \, m$ deep.

$A$ toy is in the form of a cone of radius $3.5 \, cm$ mounted on a hemisphere of the same radius. The total height of the toy is $15.5 \, cm$. Find the total surface area of the toy (in $cm^2$). $\left[ \text{Use } \pi = \frac{22}{7} \right]$

$A$ cylindrical bucket,$32 \, cm$ high and with a base radius of $18 \, cm$,is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is $24 \, cm$,find the radius and slant height of the heap. [Take $\pi = \frac{22}{7}$]

$A$ solid iron pole consists of a cylinder of height $220 \,cm$ and base diameter $24 \,cm$,which is surmounted by another cylinder of height $60 \,cm$ and radius $8 \,cm$. Find the mass of the pole,given that $1 \,cm^3$ of iron has approximately $8 \,g$ mass. (in $kg$) (Use $\pi = 3.14$)

$A$ gulab jamun contains sugar syrup up to about $30\%$ of its volume. Find approximately how much syrup would be found in $45$ gulab jamuns,each shaped like a cylinder with two hemispherical ends with length $5\,cm$ and diameter $2.8\,cm$ (see figure) (in $cm^3$) [take $\pi=\frac{22}{7}$].

Vedclass Test Series

Exam Paper Generator

Online Exam Module