Water Tank Volume Calculation: Composite Prism

The water tank consists of two prism parts: a bottom triangular prism and a top rectangular prism. To find the total volume in liters, we calculate the volume of each part in cubic meters, sum them, and then convert to liters using the given factor ($1 \text{ m}^3 = 1000 \text{ L}$).

Triangular Prism Volume Calculation

The volume ($V$) of a prism is calculated using the formula: $V = \text{Base Area} \times \text{Height}$.

• Base Area ($A_{triangle}$) = 60 cm²
• Convert the base area to square meters: $A_{triangle} = 60 \text{ cm}^2 = 60 \times (10^{-2} \text{ m})^2 = 60 \times 10^{-4} \text{ m}^2 = 0.006 \text{ m}^2$.
• Height ($h_{triangle}$) = 1.2 m
• Volume of the triangular prism: $V_{triangle} = A_{triangle} \times h_{triangle} = 0.006 \text{ m}^2 \times 1.2 \text{ m} = 0.0072 \text{ m}^3$.

Rectangular Prism Volume Calculation

The volume ($V$) of a rectangular prism is calculated using the formula: $V = \text{Length} \times \text{Width} \times \text{Height}$.

• Base dimensions: 40 cm × 30 cm. Convert these to meters: Length ($l_{rect}$) = 0.4 m, Width ($w_{rect}$) = 0.3 m.
• Height ($h_{rect}$) = 0.8 m
• Volume of the rectangular prism: $V_{rect} = l_{rect} \times w_{rect} \times h_{rect} = (0.4 \text{ m} \times 0.3 \text{ m}) \times 0.8 \text{ m} = 0.12 \text{ m}^2 \times 0.8 \text{ m} = 0.096 \text{ m}^3$.

Total Composite Volume Calculation

Add the volumes of the two prisms to find the total volume in cubic meters.

• Total Volume ($V_{total}$) = $V_{triangle} + V_{rect}$
• $V_{total} = 0.0072 \text{ m}^3 + 0.096 \text{ m}^3 = 0.1032 \text{ m}^3$.

Volume Conversion to Liters

Convert the total volume from cubic meters to liters using the conversion factor $1 \text{ m}^3 = 1000 \text{ L}$.

• Total Volume in Liters = $V_{total} \times 1000 \text{ L/m}^3$
• Total Volume in Liters = $0.1032 \text{ m}^3 \times 1000 \text{ L/m}^3 = 103.2 \text{ L}$.