Word Problems: Surface Area & Volume of Prisms

The volume (V) of a rectangular prism is calculated using the formula: $$V = lwh$$ , where l is the length, w is the width, and h is the height.

The surface area (SA) of a rectangular prism is calculated using the formula: $$SA = 2(lw + lh + wh)$$ , where l is the length, w is the width, and h is the height.

Using the formula $$SA = 2(lw + lh + wh)$$ , the surface area is $$SA = 2(4*3 + 4*2 + 3*2) = 52 in^2$$ .

Using the formula $$V = lwh$$ , the volume is $$V = 8*5*2 = 80 cm^3$$ .

To find the cost, calculate the area using $$A = lw$$ , then multiply the area by the cost per square yard.

The volume of water needed is calculated as $$V = lwh = 30*15*(8-2) = 3600 ft^3$$ .

Leaving space unfilled prevents overflow and allows for water displacement when people enter the pool.

Common units for volume include cubic centimeters (cm³), cubic meters (m³), liters (L), and cubic feet (ft³).

Surface area is typically measured in square units such as square centimeters (cm²), square meters (m²), and square feet (ft²).

The volume of a prism increases with the increase in any of its dimensions (length, width, height).