Question

1. A 890 kg culvert is made of a hollow cylindrical material with outer radius of 76cm and an inner radius of 62cm. It crosses a road of width 3m. Determine the density of the material used in its construction in Kg/m3 correct to one decimal place.

Answer 1

Given:

A 890 kg culvert is made of a hollow cylinder with outer radius 76 cm and inner radius of 62 cm.It crosses a road of width 3 m.

To Find:

Density of the material correct upto 1 decimal place.

Solution:

Mass of culvert = 890 kg.

Outer radius of cylinder = 76 cm

inner radius of cylinder = 62 cm

length of hollow cylinder = 3 m

Volume of a hollow cylinder

$V = \pi (R^{2} - r^{2} )h$

R = .76 m  r = .62 m   h = 3 m

Volume of a cylinder

$V = \pi (.76^{2} - .62^{2} )3\\V = 1.8 {m^{3} }$

Density of a material

$\rho = \frac{M}{V}\\ \rho = \frac{890}{1.8}\\ \rho= 494.4 \frac{kg}{m^{3} }$

Density of material is 494.4 kilogram per cubic meter.