by: misha, simran, and malika. vocabulary ●altitude- height of the pyramid or cone from base to...

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!