A porch roof that slopes upward at 45° measures 3.0 m × 5.0 m.It is covered with a slab of insulating material that is 2.0 cm thick.If the density of the insulation is 15 kg/m³,what is the weight of the insulation,in pounds,on the roof? (1.00 kg weighs 2.2 lb and density is mass per unit volume. ) A)4.5 lb B)9.0 lb C)20 lb D)990 lb E)9.9 lb

Question

Quizplus · Accepted Answer

First, calculate the volume of the insulation. The area of the roof is not directly given but can be inferred from the dimensions provided. However, the slope of the roof or its dimensions are not necessary for calculating the volume of the insulation because the thickness is uniform across the entire roof. The volume of the insulation is the area of the roof (3.0 m × 5.0 m = 15.0 m²) multiplied by the thickness of the insulation (2.0 cm = 0.02 m), giving a volume of 0.3 m³. Using the density of the insulation (15 kg/m³), the mass of the insulation is density × volume = 15 kg/m³ × 0.3 m³ = 4.5 kg. To convert the mass to pounds, multiply by the conversion factor (2.2 lb/kg), resulting in 4.5 kg × 2.2 lb/kg = 9.9 lb.

A Porch Roof That Slopes Upward at 45° Measures 3