Find the volume of the composite solid

Question

asked Dec 9, 2020 84.5k views

2 Answers

MAXE · Answer 1 · 2020-12-12T18:27:02+0000

Answer:

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

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

$V=(1)/(3)\pi r^2H$

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

$H^2=12.96\to H=√(12.96)\\\\H=3.6\ yd$

Calculate the volume:

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

The volume of the composite solid:

V=V_R+V_C

Substitute:

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