Question

Find the volume of the composite solid

Answer 1

Its A. 244.36 yd on edg

Explanation:

I took the quiz and got it right

Answer 2

`\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`