A metallic sphere of radius 21 ,cm is melted | vedclass

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

Question

(D) Radius of the sphere $R = 21 \,cm$.Volume of the sphere $= \frac{4}{3} \pi R^3 = \frac{4}{3} \pi (21)^3 \,cm^3$.For the cylindrical wire,diameter

Vedclass · Accepted Answer

$1975.68$

Vedclass · Answer

(D) Radius of the sphere $R = 21 \,cm$.Volume of the sphere $= \frac{4}{3} \pi R^3 = \frac{4}{3} \pi (21)^3 \,cm^3$.For the cylindrical wire,diameter $= 0.5 \,cm$,so radius $r = \frac{0.5}{2} = 0.25 = \frac{1}{4} \,cm$.Let the length of the wire be $h \,cm$.Volume of the wire $= \pi r^2 h = \pi (\frac{1}{4})^2 h \,cm^3$.Since the sphere is recast into a wire,their volumes are equal:$\pi (\frac{1}{4})^2 h = \frac{4}{3} \pi (21)^3$$\frac{1}{16} h = \frac{4}{3} 	imes 21 	imes 21 	imes 21$$h = 16 	imes 4 	imes 7 	imes 21 	imes 21$$h = 64 	imes 7 	imes 441 = 197568 \,cm$.To convert into meters,divide by $100$:$h = \frac{197568}{100} = 1975.68 \,m$.Thus,the length of the wire is $1975.68 \,m$.

$A$ metallic sphere of radius $21 \,cm$ is melted and recast to form a wire with diameter $0.5 \,cm$. Find the length of the wire in $m$.

Similar Questions

$A$ solid iron cuboidal block of dimensions $4.4 \, m \times 2.6 \, m \times 1 \, m$ is recast into a hollow cylindrical pipe of internal radius $30 \, cm$ and thickness $5 \, cm$. Find the length of the pipe in meters.

........ litres of water at the most can be stored in a cubical tank with length $1\, m$.

The volume of a sphere with diameter $10 \, cm$ is $\ldots \ldots \, cm^3$.

The ratio of radii of two spheres is $2:3$. Then,the ratio of their volumes is $\ldots \ldots \ldots \ldots$.

$A$ farmer connects a pipe of internal diameter $20 \,cm$ from a canal into a cylindrical tank in her field,which is $10 \,m$ in diameter and $2 \,m$ deep. If water flows through the pipe at the rate of $3 \,km/h$,in how much time will the tank be filled? (in $minutes$) [Take $\pi = \frac{22}{7}$]

Vedclass Test Series

Exam Paper Generator

Online Exam Module