Final answer:
The density of the culvert material is calculated by finding the volume of the hollow cylindrical culvert and then dividing the mass by this volume. The volume is obtained by subtracting the volume of the inner cylinder from that of the outer cylinder.
Step-by-step explanation:
To determine the density of the material used in the construction of an 890kg culvert with an outer radius of 76cm and an inner radius of 64cm, we need to calculate the volume and then use the mass to find the density. The formula for the volume of a cylinder is πr²h, where π is Pi (approximately 3.14159), r is the radius, and h is the height. Since the culvert is hollow, we must calculate the volume of the outer cylinder and subtract the volume of the inner cylinder.
The volume of the outer cylinder (πr²h) with r = 0.76m and h = 3m is:
V_outer = π × (0.76m)² × 3m
The volume of the inner cylinder (πr²h) with r = 0.64m and h = 3m is:
V_inner = π × (0.64m)² × 3m
The total volume (V_total) of the culvert is the volume of the outer cylinder minus the volume of the inner cylinder:
V_total = V_outer - V_inner
Once V_total is calculated, we can find the density (ρ) using the mass (m = 890kg) with the formula:
ρ = m / V_total
After performing the calculations, we round the density to one decimal place as requested.