Question

A town's public works department has ordered sand to spread on roadways during the upcoming winter snows. The delivered sand forms a right cone 36 feet high and a base diameter of 54 feet. How many cubic yards of sand has the department received?

Answer 1

A cone is 1/3 of a cylinder the formula is

V = (1/3) pi * r^2 * h

so we have

V = (1/3) * pi * 27^2 * 36
= 27482.65253 cubic feet

Answer 2

However, 27 cubic feet = 1 cubic yard so

27482.65253/27 = 1017.87602 cubic yards

Answer 3

oh thanks can you help me with quite a few more please

Answer 4

A contractor has installed a silt fence around an area that is semi-circular and level to prevent soil from the construction site entering nearby streams. The diameter of the semi-circle is 1200 feet. How many linear feet of fence does the contractor need to use to enclose the area?

Answer 5

Does the fence connect the two ends of the semicircles?

Answer 6

semicircle*

Answer 7

Anyways, you'd find the circumference of a circle (2*pi*r). Semi-circle is half of a circle so you can use (pi*r). The radius is 600 ft, so for the semi-circular part of the fence you'd need approximately 1884.96 linear ft of fence. If you connect the two ends of the semi-circle, add another 1200 linear feet so you'd have 3084.96 linear ft.

Answer 8

oh ok thanks

Answer 9

how many acres would be enclosed by the fence?

Answer 10

You find the area of the semicircle then. (pi * r^2)/2. Then convert to acres.
1 acre = 43,560ft^2

Answer 11

oh wow thanks once again. i have about 3 more questions, do you have the time?

Answer 12

Just post them, I'm sure someone will answer.