Date post: | 22-Jan-2016 |
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By: Misha, Simran, and Malika
Vocabulary● Altitude- height of the pyramid or cone from base to vertex● Vertex- special kind of point that described the corners or intersections of geometry● Radius- length of a line segment from its center to its perimeter● 30°-60°-90°- special right triangle● 45°-45°-90°- special right triangle
Formulas● Pyramids: ⅓Bh● Cones: ⅓πr²h
Square-base Pyramid Problems
● Square-based Pyramid
Find the volume of the
pyramid using the
formulaSubstitute in the numbers for the formula (B=area of the base)
Square-base Pyramid Problems
After plugging in all the
numbers multiply them
together
After multiplying, divide by 3 and then get your final answer
Square-based Pyramid (Trig)
● Use trigonometry to find the volume of the square based pyramid
Now you must use trig to find the volume of the square based pyramid
When the square is split in
half by the diagonal it creates
a 45°-45°-90° triangle. Use
this to solve for the area of
the base
Square-based Pyramid (Trig)
If the trigonometry (with the 45°-45°-90° triangle) was used correctly, and the rest of the formula was substituted correctly then the final answer should have been 33.3 meters cubed.
Triangular-based Pyramid
● Triangular-based PyramidFind the volume of the Triangular-based pyramid using the formula
Remember that the base is now a
triangle
Triangular-based Pyramid
Start to substitute all the numbers but do not forget to divide by two for area of the triangular base
Multiply all numbers together before dividing by 3
Triangular-based Pyramid
Here is the final answer: If all the steps were done correctly, your final answer should have been 272 units cubed.
Triangular-based Pyramid (Trig)
● Use trigonometry to find the volume of the Triangular-based Pyramid
Use the 30-60-90 special triangle values to solve this problem
Triangular-based Pyramid (Trig)
Be sure to divide by two because of the triangular base and if everything is done right the final answer should be 41.569 units cubed.
Cones● Use the formula to find the volume of the cone
Find the area of the base using 3.14xr*2 and then multiply by the height.
The final a
nswer s
hould be
91.4 units cu
bed.
Cones (Trig)● Cones with trigonometry
Use Tan=opposite/adjacent to solve this
The final answer should
be 1482.18 units cubed
Cones (Trig 2)
Use the pythagorean theorem to determine the altitude of the cone and then substitute the numbers into the formula and find the volume.
THE END!