Can someone please help me please

Mathematics

1 answer:

Assoli18 [71]3 years ago

6 0

A
Volume of the Cylinder
Givens
H = 60 yards.
Diameter = 20 yards
pi = 3.14

Formula
V = pi * r^2 * h

Calculations
r = d/2
r = 32/2
r = 16

V = 3.14 * 16^2 * 60
V = 48230 cubic yards [Cylinder's Volume]

Cone
Formula
V = 1/3 pi r^2 H

Givens
pi = 3.14
r = 16 yards
h = 20 yards

Sub and solve
V = 1/3 3.14 * 16^2 * 20
V = 5359 cubic yards.

Total Volume of the structure
48230 + 5359 = 53589 Cubic Yards

Water Content
The answer to this part requires a proportion.

1 Cubic yard will hold 201.97 gallons.
53589 yd^3 = x

1/201.97 = 53589 /x [ You should get a pretty big answer]
x = 201.87 * 53589
x = 10 819 092 gallons can be held by the tank.

10 819 092 gallons <<<< answer

B
If the height of both the cylinder and the cone remain the same. If the radius doubles in both the cylinder and the cone then the tank will hold 4 times as much.

Total volume before doubling the radius = pi * r^2 h + 1/3 pi r^2 h
New Total Volume = pi * (2*r)^2 h + 1/3 pi * (2r)^2 h
New Total volume = pi * 4r^2 h + 1/3 pi *4 r^2 h
New Total Volume = 4 [pi r^2 h + 1/3 pi r^2 h]
but pi r^2 h + 1/3 pi r^2 h is the total volume before doubling the radius

New volume = 4 original volume. <<<<< answer to part B

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