An open rectangular cistern when measured from outside is 1.15 m long, 0.94 m broad and 70 cm deep. It is made up of iron, which is 5 cm thick. Find
(i) The capacity of cistern.
(ii) Volume of iron used.

Options

A. `{:(""(i),(ii)),("756700 cm"^(3),"573300 cm"^(3)):}`
B. `{:(""(i),(ii)),("756700 cm"^(3),"529200 cm"^(3)):}`
C. `{:(""(i),(ii)),("529200 cm"^(3),"227500 cm"^(3)):}`
D. `{:(""(i),(ii)),("573300 cm"^(3),"183400 cm"^(3)):}`

Answer

To solve the problem, we need to find two things:

1. The capacity of the cistern.
2. The volume of iron used to construct the cistern.

### Step 1: Convert all measurements to the same unit
The dimensions given are in meters and centimeters. To make calculations easier, we will convert everything to meters.

- Length = 1.15 m (already in meters)
- Breadth = 0.94 m (already in meters)
- Depth = 70 cm = 70/100 = 0.70 m
- Thickness of iron = 5 cm = 5/100 = 0.05 m

### Step 2: Calculate the internal dimensions of the cistern
Since the cistern is made of iron which is 5 cm thick, we need to subtract twice the thickness from each external dimension to find the internal dimensions.

- Internal Length = External Length - 2 × Thickness
\[ = 1.15 m - 2 \times 0.05 m = 1.15 m - 0.10 m = 1.05 m \]

- Internal Breadth = External Breadth - 2 × Thickness
\[ = 0.94 m - 2 \times 0.05 m = 0.94 m - 0.10 m = 0.84 m \]

- Internal Depth = External Depth - Thickness (since it is open from the top)
\[ = 0.70 m - 0.05 m = 0.65 m \]

### Step 3: Calculate the capacity of the cistern
The capacity of the cistern can be calculated using the formula for the volume of a rectangular prism:
\[ \text{Volume} = \text{Length} \times \text{Breadth} \times \text{Height} \]
Substituting the internal dimensions:
\[ \text{Capacity} = 1.05 m \times 0.84 m \times 0.65 m \]
Calculating this:
\[ = 1.05 \times 0.84 \times 0.65 = 0.5733 \, m^3 \]

### Step 4: Calculate the volume of iron used
To find the volume of iron used, we first calculate the volume of the external dimensions and then subtract the internal volume from it.

- External Volume = External Length × External Breadth × External Depth
\[ = 1.15 m \times 0.94 m \times 0.70 m \]
Calculating this:
\[ = 1.15 \times 0.94 \times 0.70 = 0.7583 \, m^3 \]

- Internal Volume (calculated previously) = 0.5733 m³

Now, we can find the volume of iron:
\[ \text{Volume of Iron} = \text{External Volume} - \text{Internal Volume} \]
\[ = 0.7583 m^3 - 0.5733 m^3 = 0.1850 m^3 \]

### Final Answers:
(i) The capacity of the cistern is **0.5733 m³**.
(ii) The volume of iron used is **0.1850 m³**.