Notes for Frustums
A frustum of a cone is the part that remains when the A frustum of a pyramid is the part that remains when vertex is cut off by a plane parallel to its base. the vertex is cut off by a plane parallel to its base. Original is Square-based Pyramid
26 in,. ? cm.
24 cm. 12 cm 10 in.
12 cm 20 in. 18 cm ? cm
18 cm 1. How is the cut-off pyramid related to the original 1. How is the cut-off cone related to the original cone? pyramid? ______2. What is the similarity ratio for the two pyramids? 2. What is the similarity ratio for the two cones? ______
3. Use the similarity ratio to find the height of the 3. What is the ratio of the volume of the cut-off cutoff cone. ______pyramid to the original pyramid? ______
4. What is the height of the frustum? ______4. If the volume of the original pyramid is 256 cm.3, find the volume of the cut-off pyramid. ______5. Can you find the surface area of the frustum by What is the volume of the frustum? ______subtracting the surface area of the cut-off cone from the surface area of the original cone? ______5. What is the ratio of the volume of the frustum to the Why or why not? ______original pyramid? ______
6. Can you find the volume of the frustum by 6. The ratios in (3) and (5) must add up to ______. subtracting the volume of the cut-off cone from the volume of the original cone? ______7. What shape are the lateral faces of the frustum? ______7. Find the volume of the frustum to the nearest tenth. 8. If the lateral edge of the original pyramid is 26 in., find the height of the trapezoidal lateral faces. ______. Find the LA for the frustum. ______8. If you cut along the slant height of the original cone and then unwrap the lateral area of the frustum, what shape will it be? ______Find the lateral area of the frustrum. ______
9. Find the surface area of the frustum. ______
Example 1 Find the exact volume and find the surface area to the nearest whole number.
3 cm
10 cm
8 cm
Example 2 Find the exact volume and the surface area to the nearest whole number.
8 cm.
9 cm.
12 cm.
Example 3 - A frustum is formed by slicing a cone Example 4 – A frustum is formed by slicing a parallel to its base. The ratio of the heights of the square-based pyramid parallel to its base and cutoff cone to the original cone is 3:5. If the volume bisecting the height of the pyramid. If the lateral of the original cone is 625 cu. in., what is the volume area of the original pyramid is 400 sq. in., what is of the frustum? the lateral area of the frustum?