9 Find the volume of the following object 60 ft 40 ft 80 ft

9. Find the volume of the following object. 60 ft 40 ft 80 ft

Solution

This is compound figure with Rectangular prism at bottom and triangular prism at top.

Volume of rectangular prism, Formula is : V=w x h x l = 40x40x80=12800 Cu Ft.

To find height of triangular prism, use Pythagoras theorem. Drop a perpendicular from triangular prism top vertex letus call this as A, intersecting point on base as B and right end point of the triangle as C.

Then AC^2=AB^2+BC^2

AB^2=AC^2-BC^2 = 60^2 - 20^2 = 3200 i.e. AB=SQRT 3200 = 56.5685 ft

Volume of Triangular prism, Formula is : V=1/2 Height x Base width x Length =1/2x56.5685x20x80=45254.80 Cu Ft

Total Volume = 12800+45254.8 = 58054.8 Cu Ft