A well of diameter 3 , m is dug 14 , m deep. | vedclass

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

Question

(D) The shape of the well is cylindrical.Depth $(h_1)$ of the well $= 14 \, m$.Radius $(r_1)$ of the circular end of the well $= \frac{3}{2} \, m = 1.

Vedclass · Accepted Answer

$1.125$

Vedclass · Answer

(D) The shape of the well is cylindrical.Depth $(h_1)$ of the well $= 14 \, m$.Radius $(r_1)$ of the circular end of the well $= \frac{3}{2} \, m = 1.5 \, m$.Width of the embankment $= 4 \, m$.The embankment is in the shape of a hollow cylinder (circular ring) with inner radius $r_1 = 1.5 \, m$ and outer radius $r_2 = r_1 + 	ext{width} = 1.5 + 4 = 5.5 \, m = \frac{11}{2} \, m$.Let the height of the embankment be $h_2$.Volume of soil dug from the well = Volume of earth used to form the embankment.$\pi 	imes r_1^2 	imes h_1 = \pi 	imes (r_2^2 - r_1^2) 	imes h_2$$\pi 	imes (1.5)^2 	imes 14 = \pi 	imes ((5.5)^2 - (1.5)^2) 	imes h_2$$2.25 	imes 14 = (30.25 - 2.25) 	imes h_2$$31.5 = 28 	imes h_2$$h_2 = \frac{31.5}{28} = 1.125 \, m$.Therefore,the height of the embankment is $1.125 \, m$.

$A$ well of diameter $3 \, m$ is dug $14 \, m$ deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width $4 \, m$ to form an embankment. Find the height of the embankment (in $m$). Take $\pi = \frac{22}{7}$.

Similar Questions

The area of the base of a cone is $60 \, cm^{2}$ and its height is $15 \, cm$. Then,the volume of the cone is $\ldots \ldots \ldots \, cm^{3}$.

The ratio of the diameters of two cylinders is $3:4$ and the ratio of their heights is $4:5$. Then,the ratio of their volumes is ..... .

Water flows through a cylindrical pipe,whose inner radius is $1 \,cm$,at the rate of $80 \,cm/sec$ into an empty cylindrical tank,the radius of whose base is $40 \,cm$. What is the rise of water level in the tank in half an hour? (in $cm$)

The radii of two $10 \, cm$ high metallic cylinders are $3.5 \, cm$ and $7 \, cm$. These cylinders are melted and recast to produce a cylinder with height $50 \, cm$. Find the radius of this new cylinder (in $cm$).

The volume of a hemisphere with diameter $1 \, cm$ is $\ldots \ldots \, cm^3$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module