Question

Find the volume of the composite solid

Answer 1

Answer:

$\large\boxed{V=(157.5+27.648\pi)\ yd^3}$

Step-by-step explanation:

We have the rectangular prism and the cone.

The formula of a volume of

1) a rectangular prism

$V=lwh$

l - length

w - width

h - height

2) a cone

$V=\dfrac{1}{3}\pi r^2H$

r - radius

H - height

We have:

1)

l = 7yd, w = 5yd, h = 4.5yd

Substitute:

$V_R=(7)(5)(4.5)=157.5\ yd^3$

2)

r = 4.8yd, l = 6yd

l - slant height

Use the Pythagorean theorem to calculate H :

$H^2+r^2=l^2$

Substitute:

$H^2+4.8^2=6^2$

$H^2+23.04=36$           subtract 23.04 from both sides

$H^2=12.96\to H=\sqrt{12.96}\\\\H=3.6\ yd$

Calculate the volume:

$V_C=\dfrac{1}{3}\pi(4.8)^2(3.6)=\dfrac{82.944}{3}\pi=27.648\pi\ yd^3$

The volume of the composite solid:

$V=V_R+V_C$

Substitute:

$V=(157.5+27.648\pi)\ yd^3$