How many sphere 12 cm in diameter can be made from a metallic cylinder of diameter 8 cm and height 90 cm ?

Answer

To find out how many spheres of 12 cm in diameter can be made from a metallic cylinder of diameter 8 cm and height 90 cm, we will follow these steps:

### Step 1: Calculate the radius of the sphere and the cylinder
- The diameter of the sphere is 12 cm, so the radius (r) of the sphere is:
\[ r = \frac{12}{2} = 6 \text{ cm} \]
- The diameter of the cylinder is 8 cm, so the radius (R) of the cylinder is:
\[ R = \frac{8}{2} = 4 \text{ cm} \]

### Step 2: Calculate the volume of the cylinder
- The formula for the volume (V) of a cylinder is given by:
\[ V = \pi R^2 h \]
- Substituting the values of R and height (h = 90 cm):
\[ V = \pi (4)^2 (90) = \pi (16)(90) = 1440\pi \text{ cm}^3 \]

### Step 3: Calculate the volume of one sphere
- The formula for the volume (V) of a sphere is given by:
\[ V = \frac{4}{3} \pi r^3 \]
- Substituting the radius of the sphere (r = 6 cm):
\[ V = \frac{4}{3} \pi (6)^3 = \frac{4}{3} \pi (216) = 288\pi \text{ cm}^3 \]

### Step 4: Calculate the number of spheres that can be made
- Let \( n \) be the number of spheres that can be made from the cylinder. The total volume of the spheres will equal the volume of the cylinder:
\[ n \times \text{Volume of one sphere} = \text{Volume of the cylinder} \]
\[ n \times 288\pi = 1440\pi \]
- Dividing both sides by \( \pi \):
\[ n \times 288 = 1440 \]
- Solving for \( n \):
\[ n = \frac{1440}{288} = 5 \]

### Final Answer
Thus, the number of spheres that can be made from the metallic cylinder is **5**.

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