Question

how many solid cylinders of radius 5cm and height 3cm can be made by using a solid sphere of radius 15cm ​

Answer 1

60 Cylinder can be made by using a solid sphere of radius 15cm .

Given :-

• Radius of Cylinder = 5cm .
• Height of Cylinder = 3 cm .
• Radius of Sphere = 15 cm .

To find :-

• Numbers of Cylinders be made by Solid Sphere of radius 15 cm .

Formula used :-

• Volume of Cylinder = πr²h .
• Volume of Sphere = 4/3πr³ .

Solution :-

Volume of Cylinder = $\sf \: \dfrac{22}{7} \times 5 \times 5 \times 3$

$\sf : : \implies \dfrac{22}{7} \times 75 \\ \\ \sf : : \implies \dfrac{1650}{7} \: {cm}^{3}$

Now, Volume of Sphere = $\sf\dfrac{4}{3} \times \dfrac{22}{7} \times 15 \times 15 \times 15$

$\sf : : \implies \: 4 \times \frac{22}{7} \times 5 \times 15 \times 15 \\ \\ \sf : : \implies \: \frac{99000}{7} \: {cm}^{3}$

Numbers of Cylinders made by Sphere $\implies\sf \: \: \:\: \: \:\: \: \: \: \: \: \: \: \: \dfrac{volume \: of \: sphere \: }{volume \: of \: cylinder }$

$\sf \: no. \: of \: cylinder \: = \dfrac{ \dfrac{99000}{ \cancel7} }{ \dfrac{1650}{\cancel7} } \\ \\ \sf \: no. \: of \: cylinder \: = \: \frac{9900\cancel0}{165 \cancel0} \\ \\\sf \: no. \: of \: cylinder \: = \: 60$

Hence, Number of Cylinder made by Sphere is 60 .