This evergreen tree is 20 feet tall with a 1-foot wide trunk. The lowest branches are 3 ft above the ground, and at that level,
the lowest branches of the tree are 7 feet wide. Determine 2 figures that can be used to estimate the volume of the tree. Indicate the dimensions of the 2 figures and estimate the volume of the tree to the nearest whole cubic foot. Will give Brainliest if answered correctly with explanation
2 answers:
Answer:
1792 cubic feet
Step-by-step explanation:
Formula to calculate the content of a cone with radius r and height h:
content cone = 1/3 * surface area * height = 1/3 * π r^2 * h
However, I estimate this tree to be like the shape of a trunced cone.
Think of it as a bucket or flower pot, see the picture.
The content of a truncated cone is: ⅓ π h (R^2 + Rr + r^2 )
with these measurements (in feet):
h = 20.0
r = 0.5
R = 7.5
Fill in these numbers in the formula and you get:
(1 / 3) * pi * 20 * (7.5^2 + (7.5 * 0.5) + 0.5^2)
1261.8730491919002841158284256173
So the trunced cone measures
1261.87 cubic feet.
Please do not forget to add the contents of a cylinder below the (trunked) cone...
The content of that cylinder is: π h R^2
Use these measurements (in feet):
R = 7.5
h = 3.0
Fill in these numbers in the formula and you get:
pi * 3 * (7.5^2)
530.14
Just add both numbers to get the total amount in cubic feet:
1261.87 + 530.14 = 1792.01
Round to nearest whole cubic foot, I estimate the volume of the tree to be 1792 cubic feet.
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