# Math question, need help with garden.?

| March 4, 2014 |

Question by C. M.: Math question, need help with garden.?
I’m moving into a new house. I want a circular flower garden in the middle of the yard. In the centre I want a pond where I’ll keep fish, water plants, etc. I’ll give you the dimensions:

It will be 10 feet away from the deck.
The total diameter of the garden/and pond is 10 feet.
The middle pond of the circular garden is 6 feet in diameter.
The outer 2 feet is the garden part.

I know I need to:
1. Excavate the pond to a depth of 3 feet (flat bottom).
2. Line the pond basin with a pond liner.
3. Add 2 inches of topsoil to the flower bed.

Supplies and services (I can only get these in the whole units):
1. Excavation: \$ 1.49 per cubic foot + 6% GST (Canadian federal tax)
2. Soil: \$ 1.99 per 1 ft(cubed) bag + 6% GST & 7% PST (Canadian Provincial Tax)
3. Pond Liner: \$ 75.00 + 6% GST & 7% PST.

Any help with this is much appreciated!

I’m assuming your question is: How much is this going to cost?

Excavation:
I’m assuming the hole dug for the pond will be dug straight down, ie the pond volume will be like a circular tank and not a half-sphere.
Volume to be excavated = pi (6ft/2)^2 (3ft) = 84.8 ft^3
E = (\$ 1.49/ft^3)( 85 ft^3)(1.06) = \$ 134.25

Soil:
If you “unravel” the donut, the volume of soil is a rectangular solid with height 2 inches, width = circumference of pond, length = circumference of garden. Volume = hwL. Circumference = pi * diameter.
V = (2/12 ft) pi (6 ft) pi (10 ft) = 98.7 ft^3
S = (\$ 1.99/ft^3)(99 ft^3) (1.13) = \$ 222.62

Pond Liner:
P = \$ 75 (1.13) = \$ 84.75

Answer: E + S + P = \$ 441.62 