Question

a solid metallic sphere of radius 7cm is melted and recast into a cylinder of radius of 3.5 cm, find the hight of the cylinder​

Answer 1

Answer:

The solid cylinder with a 7 cm radius and 14 cm height has a volume of v1= π*49*14 cubic cm. A sphere with a 3.5 cm radius has a volume of v2 = (4/3)*π*3.5^3 cubic cm. The number of solid spheres is then v1/v2 or 49*14/(4/3)*3.5^3 or 12

Step-by-step explanation:

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Answer 2

QUESTION-:

a solid metallic sphere of radius 7 cm is melted and recast into a cylinder of radius of 3.5 cm, find the height of the cylinder​

EXPLANATION-:

GIVEN-:

r₁(radius of sphere)=7 cm

r₂(radius of cylinder)=3.5 cm

h(height of cylinder)= ?           [TO BE CALCULATED]

In the case -:

$\longrightarrow \underline{\boxed{\ddag\; \tt Volume_{(Sphere)}=Volume_{(cylinder)} }}$

We know that-:

$\rightarrow \boxed{\bf\; \dag\;Volume_{(sphere)}=\frac{4}{3}\pi r^3}$

And -:

$\rightarrow \boxed{\bf\; \dag Volume_{(Cylinder)}= {\pi}r^2h}$

Now equating both volumes we have-:

$\rightarrow \bf\; \frac{4}{3}\pi (7)^3={\pi}(3.5)^2h\\\\\rightarrow \bf\; \frac{4}{3} \times 343=12.25h\\\\\rightarrow \bf\; \frac{1372}{3}=12.25h\\\\\rightarrow \bf\; \frac{1372}{3}\times \frac{1}{12.25}=h\\\\\longrightarrow \underline{\boxed{\sf\; h \approx 37.34\;cm}}$

∴The height of cylinder is 37.34 cm (approx)