Question

Find the volume of the composite solid. Round your answer to the nearest hundredth.

A. 239.23cm^3

B.246.08 cm ^3

C. 294.03 cm ^3

D. 308.78 cm^3

Answer 1

to answer you need to fing the rectangular shape first so :

l×w×h

6.2*6.7*5.5= 228.47 cm cube

take away the top so

228.47-(6.2*6.7)
22.8.47-41.54
186.93 cm cube

then do the volume of pyramid : ( make sure to not add the base)

the answer is c

Answer 2

C.
`294.03 cm ^3`

Step-by-step explanation:

We must find two volumes, that of the quadrangular prism and that of the pyramid of the top and finally add them to get the total volume.

Quadrangular prism volume:

`V_(1)=A_(b)*H`

where

`A_(b)` is the base area

and H is the height

`V_(1)=6.7cm*6.2cm*5.5=228.47cm^3`

Volume of the quadrangular pyramid:

`V_(2)=(A_(b)*H)/(3)`

To find the value of height H we use pitagoras:

`h=√(5.8^2-(6.7/2)^2) =4.7347cm`

Thus

`V_(2)=((6.7cm*6.2cm)*4.7347cm)/(3)=65.56cm^3`

The total volume is :

`V=V_(1)+V_(2)=228.27cm^3+65.56cm^3=294.03cm^3`

Wich is option C.