Find the capacity of a rectangular cistern in litres whose dimensions are 11.2 m × 6 m × 5.8 m. Find the area of the iron sheet required to make the cistern, if it is hammered into a sheet to cover an area of 1 hectare.

Question

Find the capacity of a rectangular cistern in litres whose dimensions are 11.2 m × 6 m × 5.8 m. Find the area of the iron sheet required to make the cistern, if it is hammered into a sheet to cover an area of 1 hectare.

Asked on March 26, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-03-26T06:46:24.869Z

i) For a cube with edge length $a = 7$ m: Step 1: Calculate the Volume ($V$). The formula for the volume of a cube is $V = a^3$. $$V = (7 \text{ m})^3$$ $$V = 7 \text{ m} \times 7 \text{ m} \times 7 \text{ m}$$ $$V = 343 \text{ m}^3$$ Step 2: Calculate the Lateral Surface Area (LSA). The formula for the lateral surface area of a cube is $\text{LSA} = 4a^2$. $$\text{LSA} = 4 \times (7 \text{ m})^2$$ $$\text{LSA} = 4 \times 49 \text{ m}^2$$ $$\text{LSA} = 196 \text{ m}^2$$ Step 3: Calculate the Total Surface Area (TSA). The formula for the total surface area of a cube is $\text{TSA} = 6a^2$. $$\text{TSA} = 6 \times (7 \text{ m})^2$$ $$\text{TSA} = 6 \times 49 \text{ m}^2$$ $$\text{TSA} = 294 \text{ m}^2$$ For $a = 7$ m: Volume: $\boxed{\text{343 m}^3}$ Lateral Surface Area: $\boxed{\text{196 m}^2}$ Total Surface Area: $\boxed{\text{294 m}^2}$ ii) For a cube with edge length $a = 5.6$ cm: Step 1: Calculate the Volume ($V$). The formula for the volume of a cube is $V = a^3$. $$V = (5.6 \text{ cm})^3$$ $$V = 5.6 \text{ cm} \times 5.6 \text{ cm} \times 5.6 \text{ cm}$$ $$V = 175.616 \text{ cm}^3$$ Step 2: Calculate the Lateral Surface Area (LSA). The formula for the lateral surface area of a cube is $\text{LSA} = 4a^2$. $$\text{LSA} = 4 \times (5.6 \text{ cm})^2$$ $$\text{LSA} = 4 \times 31.36 \text{ cm}^2$$ $$\text{LSA} = 125.44 \text{ cm}^2$$ Step 3: Calculate the Total Surface Area (TSA). The formula for the total surface area of a cube is $\text{TSA} = 6a^2$. $$\text{TSA} = 6 \times (5.6 \text{ cm})^2$$ $$\text{TSA} = 6 \times 31.36 \text{ cm}^2$$ $$\text{TSA} = 188.16 \text{ cm}^2$$ For $a = 5.6$ cm: Volume: $\boxed{\text{175.616 cm}^3}$ Lateral Surface Area: $\boxed{\text{125.44 cm}^2}$ Total Surface Area: $\boxed{\text{188.16 cm}^2}$

Accepted Answer · 2026-03-26T06:46:24.869Z

i) For a cube with edge length $a = 7$ m: Step 1: Calculate the Volume ($V$). The formula for the volume of a cube is $V = a^3$. $$V = (7 \text{ m})^3$$ $$V = 7 \text{ m} \times 7 \text{ m} \times 7 \text{ m}$$ $$V = 343 \text{ m}^3$$ Step 2: Calculate the Lateral Surface Area (LSA). The formula for the lateral surface area of a cube is $\text{LSA} = 4a^2$. $$\text{LSA} = 4 \times (7 \text{ m})^2$$ $$\text{LSA} = 4 \times 49 \text{ m}^2$$ $$\text{LSA} = 196 \text{ m}^2$$ Step 3: Calculate the Total Surface Area (TSA). The formula for the total surface area of a cube is $\text{TSA} = 6a^2$. $$\text{TSA} = 6 \times (7 \text{ m})^2$$ $$\text{TSA} = 6 \times 49 \text{ m}^2$$ $$\text{TSA} = 294 \text{ m}^2$$ For $a = 7$ m: Volume: $\boxed{\text{343 m}^3}$ Lateral Surface Area: $\boxed{\text{196 m}^2}$ Total Surface Area: $\boxed{\text{294 m}^2}$ ii) For a cube with edge length $a = 5.6$ cm: Step 1: Calculate the Volume ($V$). The formula for the volume of a cube is $V = a^3$. $$V = (5.6 \text{ cm})^3$$ $$V = 5.6 \text{ cm} \times 5.6 \text{ cm} \times 5.6 \text{ cm}$$ $$V = 175.616 \text{ cm}^3$$ Step 2: Calculate the Lateral Surface Area (LSA). The formula for the lateral surface area of a cube is $\text{LSA} = 4a^2$. $$\text{LSA} = 4 \times (5.6 \text{ cm})^2$$ $$\text{LSA} = 4 \times 31.36 \text{ cm}^2$$ $$\text{LSA} = 125.44 \text{ cm}^2$$ Step 3: Calculate the Total Surface Area (TSA). The formula for the total surface area of a cube is $\text{TSA} = 6a^2$. $$\text{TSA} = 6 \times (5.6 \text{ cm})^2$$ $$\text{TSA} = 6 \times 31.36 \text{ cm}^2$$ $$\text{TSA} = 188.16 \text{ cm}^2$$ For $a = 5.6$ cm: Volume: $\boxed{\text{175.616 cm}^3}$ Lateral Surface Area: $\boxed{\text{125.44 cm}^2}$ Total Surface Area: $\boxed{\text{188.16 cm}^2}$