Question

A solid metal sphere 3cm in radius is melted t form a cylingrical tube of length 4cm and external diameter 10cm .Find th thickness of the tube

Answer 1

Question:

A solid metal sphere 3cm in radius is melted to form a cylindrical tube of length 4cm and external diameter 10cm .Find the thickness of the tube.

Solution:

For sphere

$r = 3cm \\ Volume = \frac{4}{3} \pi {r}^{3} \\ Volume = \frac{4}{3} \times \pi \times 27 \\ Volume = 36\pi$

For cylindrical tube

$External\: radius(R)=5cm\\Internal\: radius=r \\ Height = 4cm\\Volume = \pi( {R}^{2} - {r}^{2} )h \\ Volume= \pi(25 - {r}^{2} )4$

According to the condition the volume of sphere shoruld be equal to that of the cylindrical tube .

$36\pi = \pi(25 - {r}^{2} )4 \\ 9 = 25 - {r}^{2} \\ {r}^{2} = 16 \\ r = 4cm$

Thickness of the tube

=External radius - Internal radius

=5-4

=1cm

Hence, the thickness of the tube is 1cm.

Answer 2

Step-by-step explanation:

r=3cm

Volume= 4/3 ×π×27=36π

Now, for the cylindrical tube

Exterior radii R=5cm

Interior radii =r

Height=4cm

Volume=π(R²-r²)h

= π(25-r²)×4

A/q

36π = π(25-r²)*4

=9 =25-r²

r²=16

r=4cm

Therefore thickness of tube

Exterior radii- interior radii

=5-4

=1cm