Question

Please answer I would really really appreciate it !

Answer 1

92.5 cubic units

Choice A

Explanation:

To approach this problem, separate out the composite solid figure into individual easily manageable components

At the bottom we have a rectangular prism which has a base length of 2a, a height of a and a width of c

Its volume = L X H X W = 2a·a·c= 2a²c

Plugging in values for a and c we get

Volume of rectangular prism

= 2 x (3.7)² x 2

= 54.76 cubic units

On top of this rectangular prism are two right-angled triangular prisms

The volume of a right-angled triangular prism =

Here height = b (confusing :)

base = a

width = c

So volume of each triangular prism

`=\textrm{$(1)/(2) * $ base x height x width}\\\\= (1)/(2) a * b * c\\\\ = (1)/(2) * 3.7 * 5.1 * 2\\\\= 18.87`

Since there are 2 such prisms the volume of both

= 18.87 x 2 = 37.74 cubic units

Total volume of composite solid = 54.76 + 37.74 = 92.5 cubic units