A hemispherical bowl is made of steel of 0.25 cm thickness. The inner radius of the bowl is 5 cm. The volume of steel used is ______. (Use `pi=3.14`)

Options

A. `42.15cm^(3)`
B. `40.52cm^(3)`
C. `41.25cm^(3)`
D. `40cm^(3)`

Answer

To find the volume of steel used in the hemispherical bowl, we need to follow these steps:

### Step 1: Identify the inner radius and thickness
- The inner radius of the bowl (r) is given as 5 cm.
- The thickness of the steel (t) is given as 0.25 cm.

### Step 2: Calculate the outer radius
- The outer radius (R) can be calculated by adding the thickness to the inner radius:
\[ R = r + t = 5 \, \text{cm} + 0.25 \, \text{cm} = 5.25 \, \text{cm} \]

### Step 3: Use the formula for the volume of a hemispherical shell
- The volume \( V \) of a hollow hemisphere is given by:
\[ V = \frac{2}{3} \pi (R^3 - r^3) \]

### Step 4: Calculate \( R^3 \) and \( r^3 \)
- Calculate \( R^3 \):
\[ R^3 = (5.25)^3 = 5.25 \times 5.25 \times 5.25 = 144.703125 \, \text{cm}^3 \]
- Calculate \( r^3 \):
\[ r^3 = (5)^3 = 5 \times 5 \times 5 = 125 \, \text{cm}^3 \]

### Step 5: Substitute values into the volume formula
- Substitute \( R^3 \) and \( r^3 \) into the volume formula:
\[ V = \frac{2}{3} \times 3.14 \times (144.703125 - 125) \]

### Step 6: Calculate the difference
- Calculate \( 144.703125 - 125 \):
\[ 144.703125 - 125 = 19.703125 \, \text{cm}^3 \]

### Step 7: Calculate the volume
- Now substitute this difference back into the volume formula:
\[ V = \frac{2}{3} \times 3.14 \times 19.703125 \]
- Calculate:
\[ V = \frac{2 \times 3.14 \times 19.703125}{3} \approx \frac{123.70625}{3} \approx 41.23541667 \, \text{cm}^3 \]

### Step 8: Round off the answer
- Rounding off to two decimal places, we get:
\[ V \approx 41.25 \, \text{cm}^3 \]

### Final Answer
The volume of steel used is approximately **41.25 cm³**.

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