Question

Find the volume of the composite solid.

A. 702.00in^3
B. 1218.03in^3
C. 676.01in^3
D. 811.51^3

Answer 1

The correct answer is option C. 676.01 in^3

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

Answer 2

`C.676.01 \: {in}^(3)`

step-by-step explanation :

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

Volume of the cuboid

`= L * B * H`

where

`L = 9 \: inches \\ B = 9 \: inches \\ H = 5 \: inches`

By substitution,

`\implies \: V = 5 * 9 * 9`

`\implies \: V = 405 \: {in}^(3)`

Volume of rectangular pyramid

`= (1)/(3) * base \: area * height`

`\implies \: V = (1)/(3) * \:( L * B ) * \: H`

`L = 9 \: inches \\ B = 9 \: inches \\ s= 11 \: inches`

We use the Pythagoras Theorem, to obtain,

h²+4.5²=11²

h²=11²-4.5²

h=√100.75

h=10.03

By substitution,

`\implies \: V = (1)/(3) * \:( 9 * 9 ) * \:10.0374`

we simplify to obtain

`\implies \: V =271.0098 \: {in}^(3)`

Hence the volume of the the composite solid

`=676.01\: {in}^(3)`