Frustum practice problems - page 2 of 3
Directions: Provide a careful solution to each problem, showing all steps in your work.Number of problems found: 57
- Two vases
Michaela has two vases in her collection. The first vase has the shape of a cone with a base diameter of d = 20 cm; the second vase has the shape of a truncated cone with a lower base of d1 = 25 cm and a diameter of the upper base d2 = 15 cm. Which vase c - Frustrum - volume, area
Calculate the surface and volume of a truncated rotating cone with base radii of 8 cm and 4 cm and a height of 5 cm. - Cutting cone
A cone with a base radius of 10 cm and a height of 12 cm is given. At what height above the base should we divide it by a section parallel to the base so that the volumes of the two resulting bodies are the same? Express the result in cm. - Digging a pit
The pit has the shape of a regular quadrilateral truncated pyramid. The edges of the bases are 14 m and 10 m long. The sidewalls form an angle of 135° with a smaller base. Find how many m³ of soil were excavated when digging the pit. - Quadrangular pyramid
Calculate the surface area and volume of a regular quadrilateral pyramid: sides of bases (bottom, top): a1 = 18 cm, a2 = 6 cm angle α = 60 ° (Angle α is the angle between the sidewall and the base plane.) S =? , V =? - Truncated cone
Calculate the volume of a truncated cone with base radiuses r1=19 cm, r2 = 11 cm, and height v = 5 cm. - Truncated pyramid The concrete pedestal in a regular quadrilateral truncated pyramid has a height of 12 cm; the pedestal edges have lengths of 2.4 and 1.6 dm. Calculate the surface of the base.
- Pyramid volume ratio
A regular quadrilateral pyramid with base edge length a = 15 cm and height v = 21 cm is given. We draw two planes parallel to the base, dividing the height of the pyramid into three equal parts. Calculate the ratio of the volumes of the 3 bodies created. - Truncated pyramid How many cubic metres is the volume of a regular quadrilateral truncated pyramid with base edges of one metre and 60 cm and a height of 250 mm?
- Slant surface
The surface of the rotating cone and its base area is in the ratio 18:5. Determine the volume of the cone if its body height is 12 cm. - An Elizabethan collar
An Elizabethan collar is used to prevent an animal from irritating a wound. The angle between the opening (diameter 6 inches) with a 16-inch diameter and the side of the collar is 53 degrees. Find the surface area of the collar shown. - 4B - truncated pyramid
Calculate the volume of a regular truncated quadrilateral pyramid if the base edges are 10 cm and 4 cm and the slant height of the lateral face is 5 cm. - Truncated pyramid
Find the volume and surface area of a regular quadrilateral truncated pyramid if base lengths a1 = 17 cm, a2 = 5 cm, and height v = 8 cm. - Pyramid edge calculation The foundations of a regular truncated quadrilateral pyramid are squares. The lengths of the sides differ by 6 dm. Body height is 7 dm. The body volume is 1813 dm³. Calculate the lengths of the edges of both bases.
- A concrete pedestal
A concrete pedestal has the shape of a right circular cone and a height of 2.5 feet. The diameters of the upper and lower bases are 3 feet and 5 feet, respectively. Determine the pedestal's lateral surface area, total surface area, and volume. - Pyramid soil
The pit is a regular truncated 4-sided pyramid, with 14 m and 10 m base edges and a depth of 6 m. Calculate how much m³ of soil was removed when we dug this pit. - Truncated pyramid Find the volume of a regular 4-sided truncated pyramid if a1 = 14 cm, a2 = 8 cm, and the angle that the side wall with the base is 42 degrees.
- Truncated pyramid
The truncated regular quadrilateral pyramid has a volume of 74 cm3, a height v = 6 cm, and an area of the lower base 15 cm² greater than the upper base's area. Calculate the area of the upper base. - The truncated
The truncated rotating cone has bases with radii r1 = 8 cm, r2 = 4 cm, and height v = 5 cm. What is the volume of the cone from which the truncated cone originated? - Pillar
Calculate the volume of a pillar in the shape of a regular quadrilateral frustum (truncated pyramid) with base edges a = 10 and b = 19, and height h = 28.
Do you have homework that you need help solving? Ask a question, and we will try to solve it. Solving math problems.
