Find the volume of the composite solid.
a. 702.00in^3
b. 1218.03in^3
c. 676.01in^3
d. 811.51^3

step-by-step explanation :

The volume of the composite solid = volume of the cuboid + volume of the rectangular pyramid

Volume of the cuboid

where

By substitution,

Volume of rectangular pyramid

We use the Pythagoras Theorem, to obtain,

h²+4.5²=11²

h²=11²-4.5²

h=√100.75

h=10.03

By substitution,

we simplify to obtain

Hence the volume of the the composite solid

The correct answer is option C.  676.01 in^3

Step-by-step explanation:

It is given a composite solid.

Total volume = volume of cuboid + volume of pyramid

To find the volume of cuboid

Volume of cuboid = Base area * height

Base area = side * side = 9 * 9

Volume = 9 * 9 * 5 = 405 in^3

To find the volume of pyramid

Before that we have to find the height of pyramid

Height² = Hypotenuse² - base² = 11² - 4.5² = 100.75

Height = √100.75 = 10.03

Volume of pyramid = 1/3(base area * height)

  = 1/3(9 * 9 * 10.03) = 271.01 in^3

To find the volume of solid

Volume of solid =  volume of cuboid + volume of pyramid

 = 405 + 271.01 = 676.01 in^3

Therefore the correct answer is option C.   676.01 in^3