Practice problems of the frustum
Direction: Solve each problem carefully and show your solution in each item.Number of problems found: 44
- Wooden bowls
Twenty wooden bowls in the shape of a truncated cone should be painted on the outside and inside with wood varnish. We need 0.1 l of paint to paint 200 cm². How many liters of paint do we have to buy if the bowls are 25 cm high, the bottom of the bowl has - Pit
The pit has the shape of a truncated pyramid with a rectangular base and is 0.8 m deep. The pit's length and width are the top 3 × 1.5 m bottom 1 m × 0.5 m. To paint one square meter of the pit, we use 0.6 l of green color. How many liters of paint are ne - Truncated cone
Calculate the height of the rotating truncated cone with volume V = 1354 cm³ and a base radii r1 = 9.1 cm and r2 = 5.4 cm. - Runcated pyramid teapot
The 35 cm high teapot has the shape of a truncated pyramid with the length of the edge of the lower square base a=50 cm and the edges of the rectangular base b: 20 cm and c: 30 cm. How many liters of water will fit in the teapot? - Truncated 43851
The pit has the shape of a regular truncated 4-sided pyramid, the base edges of which are 14m, 10m, and the depth is 6m. Calculate how many m³ of soil were removed when we dug this pit. - Frustum of a cone
A reservoir contains 28.54 m³ of water when complete. The diameter of the upper base is 3.5 m, while the lower base is 2.5 m. Find the height if the reservoir is in the form of a frustum of a right circular cone. - Determine 73454
The volume of the cut cone is V = 38000π cm³. The radius of the lower base is 10 cm larger than the radius of the upper base. Determine the radius of the base if height v = 60 cm. - 2x cone
Circular cone height 84 cm was cut plane parallel with the base. The volume of these two small cones is the same. Calculate the height of the smaller cone. - The surface
The surface of a truncated rotating cone with side s = 13 cm is S = 510π cm². Find the radii of the bases when their difference in lengths is 10cm. - Calculate 38701
Calculate the surface and volume of the cut rotating cone with base radii of 14cm and 8cm height of 11cm. - Flowerbed
Flowerbed has the shape of a truncated pyramid. The bottom edge of the base a = 10 m, and the upper base b = 9 m. The deviation angle between the edge and the base is alpha = 45°. What volume is needed to make this flowerbed? How many plants can be plante - Digging a pit
The pit has the shape of a regular quadrilateral truncated pyramid. The edges of the bases are 14m and 10m long. The sidewalls form an angle of 135° with a smaller base. Find how many m³ of soil were excavated when digging the pit. - 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.
- Two vases
Michaela has two vases in her collection. The first vase has the shape of a cone with a base diameter d = 20 cm; the second vase has the shape of a truncated cone with the lower base d1 = 25 cm and the diameter of the upper base d2 = 15 cm. Which vase can - Similar frustums
The upper and lower radii of a frustum of a right circular cone are 8 cm and 32 cm, respectively. If the altitude of the frustum is 10 cm, how far from the bottom base must a cutting plane be made to form two similar frustums? - 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. - Hexagon cut pyramid
Calculate the volume of a regular 6-sided cut pyramid if the bottom edge is 30 cm, the top edge is 12 cm, and the side edge length is 41 cm. - Truncated cone
Calculate the volume of a truncated cone with base radiuses r1=13 cm, r2 = 10 cm, and height v = 8 cm. - Quadrangular pyramid
Calculate the surface area and volume of a regular quadrangular pyramid: sides of bases (bottom, top): a1 = 18 cm, a2 = 6cm angle α = 60 ° (Angle α is the angle between the sidewall and the base plane.) S =? , V =? - 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.
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