Question

A metallic solid sphere of radius 9 cm is melted to form of solid cylinder of radius 9 cm find the height of the cylinder.​

Answer 1

✬ Height = 12 cm ✬

Step-by-step explanation:

Given:

• A metallic solid sphere is melted to form a solid cylinder.
• Measure of radius of sphere is 9 cm.
• Measure of radius of cylinder is 9 cm.

To Find:

• What is height of cylinder?

Solution: Since, the sphere is melted to form a solid cylinder therefore we have find volume of both and also

➯ Volume of sphere = Volume of cylinder

As we know that

★ Volume of Sphere = 4/3πr³ ★

$\implies{\rm }$ Volume = 4/3π(9)³

$\implies{\rm }$ Volume = 4/3π $\times$ 9 $\times$ 9 $\times$ 9

$\implies{\rm }$ Volume = 4π/3 $\times$ 729

$\implies{\rm }$ Volume = 4π $\times$ 243........(1)

Now,

★ Volume of Cylinder = πr²h ★

$\implies{\rm }$ Volume = π(9)²h

$\implies{\rm }$ π81h..........(2)

A/q

• Equation 1 = Equation 2

➬ 4π(243) = π(81)(h)

➬ 4(243) = 81h

➬ 972 = 81h

➬ 972/81 = h

➬ 12 cm = h

Hence, The height of cylinder is 12 cm.

Answer 2

Answer:

The height of the cylinder : 12 cm

Given:

Radius of the solid sphere = 9 cm

Radius of the solid cylinder r = 9 cm

To Find:

The height of the cylinder

Solution:

We have,

Radius of the solid sphere, R = 9 cm and

Radius of the solid cylinder, r = 9 cm

Let the height of the cylinder be h.

Now,

Volume of the cylinder = volume of the sphere

but, we know,

${\pink{\boxed{\boxed{\red{\star{\sf {Volume\:of\: cylinder \ = \pi {r}^{2} \ h}}}}}}}}$

${\pink{\boxed{\boxed{\red{\star{\sf Volume\:of\: sphere= \dfrac{4}{3} \pi {R}^{3}}}}}}}$

${\implies{\rm{\pi {r}^{2} h \ = \ \dfrac{4}{3} \pi {R}^{3}}}}}$

${\implies{\rm{\cancel{\pi} {r}^{2} h=\dfrac{4}{3} \cancel{ \pi } {R}^{3}}}}$

${\implies{\rm{ h \ = \dfrac{4{R}^{3}}{3 {r}^{2}}}}}$

${\implies{\rm{h = \dfrac{4 \times 9 \times 9 \times 9 }{3 \times 9 \times 9 }}}}}$

$\therefore{\pink{\boxed{\blue{\star{\rm{h \ = \ 12 }}}}}}$

Hence, the height of the cylinder is : 12 cm.