MATH SOLVE

3 months ago

Q:
# Find the volume of the composite solid. A. 702.00in^3B. 1218.03in^3C. 676.01in^3D. 811.51^3

Accepted Solution

A:

Answer:[tex] C.676.01 \: {in}^{3} [/tex]step-by-step explanation :The volume of the composite solid = volume of the cuboid + volume of the rectangular pyramid Volume of the cuboid [tex] = L \times B \times H[/tex]where [tex]L = 9 \: inches \\ B = 9 \: inches \\ H = 5 \: inches[/tex]By substitution, [tex] \implies \: V = 5 \times 9 \times 9[/tex][tex]\implies \: V = 405 \: {in}^{3} [/tex]Volume of rectangular pyramid [tex] = \frac{1}{3} \times base \: area \times height[/tex][tex]\implies \: V = \frac{1}{3} \times \:( L \times B ) \times \: H[/tex][tex] L = 9 \: inches \\ B = 9 \: inches \\ s= 11 \: inches[/tex]We use the Pythagoras Theorem, to obtain,h²+4.5²=11²h²=11²-4.5²h=√100.75h=10.03By substitution, [tex]\implies \: V = \frac{1}{3} \times \:( 9 \times 9 ) \times \:10.0374[/tex]we simplify to obtain [tex]\implies \: V =271.0098 \: {in}^{3} [/tex]Hence the volume of the the composite solid [tex]=676.01\: {in}^{3} [/tex]