Fresh features from the #1 AI-enhanced learning platform.Try it free
Fresh features from the #1 AI-enhanced learning platformCrush your year with the magic of personalized studying.Try it free
Question

# A planning engineer for a new alum plant must present some estimates to his company regarding the capacity of a silo designed to store bauxite ore until it is processed into alum. The ore resembles pink talcum powder and is poured from a conveyor at the top of the silo. The silo is a cylinder 100 ft high with a radius of 200 ft. The conveyor carries ore at a rate of 60,000 $\pi \mathrm{ft}^{3} / \mathrm{h}$ and the ore maintains a conical shape whose radius is 1.5 times its height. How much room will be left in the floor area of the silo when the pile is 60 ft high? How fast is the floor area of the pile growing at the height?

Solution

Verified
Step 1
1 of 5

When the pile is 60ft high, the radius of the pile is $1.5\cdot 60=90$ ft

Since the radius of the silo is 200 ft,

$\text{The floor area left} = \pi\left(\text{radius of the silo}\right)^2-\pi\left(\text{radius of the pile}\right)^2$

$\text{The floor area left} = \pi\left(200\right)^2-\pi\left(90\right)^2=31900\pi\text{ square feet}$

## Recommended textbook solutions

#### Thomas' Calculus

14th EditionISBN: 9780134438986 (7 more)Christopher E Heil, Joel R. Hass, Maurice D. Weir
10,143 solutions

#### Calculus: Early Transcendentals

10th EditionISBN: 9780470647691Howard Anton, Irl C. Bivens, Stephen Davis
10,488 solutions

#### Calculus: Early Transcendentals

8th EditionISBN: 9781285741550 (5 more)James Stewart
11,085 solutions

#### Calculus: Early Transcendentals

9th EditionISBN: 9781337613927Daniel K. Clegg, James Stewart, Saleem Watson
11,048 solutions