Answer:
[tex]\large\boxed{V=(157.5+27.648\pi)\ yd^3}[/tex]
Step-by-step explanation:
We have the rectangular prism and the cone.
The formula of a volume of
1) a rectangular prism
[tex]V=lwh[/tex]
l - length
w - width
h - height
2) a cone
[tex]V=\dfrac{1}{3}\pi r^2H[/tex]
r - radius
H - height
We have:
1)
l = 7yd, w = 5yd, h = 4.5yd
Substitute:
[tex]V_R=(7)(5)(4.5)=157.5\ yd^3[/tex]
2)
r = 4.8yd, l = 6yd
l - slant height
Use the Pythagorean theorem to calculate H :
[tex]H^2+r^2=l^2[/tex]
Substitute:
[tex]H^2+4.8^2=6^2[/tex]
[tex]H^2+23.04=36[/tex] subtract 23.04 from both sides
[tex]H^2=12.96\to H=\sqrt{12.96}\\\\H=3.6\ yd[/tex]
Calculate the volume:
[tex]V_C=\dfrac{1}{3}\pi(4.8)^2(3.6)=\dfrac{82.944}{3}\pi=27.648\pi\ yd^3[/tex]
The volume of the composite solid:
[tex]V=V_R+V_C[/tex]
Substitute:
[tex]V=(157.5+27.648\pi)\ yd^3[/tex]
