Question

A covered bridge in Vermont has the dimensions shown

What is the volume of the roof rounded to the nearest tenths?

Answer 1

The volume of the roof rounded to the nearest tenths is 2226.56 ft³

Explanation:

We note that the shape of the cross section of the roof is that of a triangle, whereby the volume in this case is the product of the length of the roof and the area of the triangular cross section as follows;

Area of the roof triangular cross section =
`(1)/(2) * Width \ of \, roof * Height \ of \, roof`

Width of the roof, W = 14.25 ft

Height of the roof, h = 2.5 ft

∴ Roof cross sectional area =
`(1)/(2) * 14.25 \ ft * 2.5 \ ft = 17.8125 \ ft^2`

Length of roof = 125 ft

Hence, volume of root = Roof cross sectional area × Roof length

∴ Volume of root = 17.8125 ft² × 125 ft = 2226.56 ft³

The volume of the roof rounded to the nearest tenths = 2226.56 ft³.