Frustum Problems

Number of problems found: 33

  • Frustrum - volume, area
    frustum-of-a-right-circular-cone Calculate the surface and volume of the truncated cone, the radius of the smaller figure is 4 cm, the height of the cone is 4 cm and the side of the truncated cone is 5 cm.
  • Frustrum - volume, area
    frustum-of-a-right-circular-cone Calculate the surface and volume of a truncated rotating cone with base radii of 8 cm and 4 cm, height 5 cm.
  • Top-open tank
    vedro The top-open tank has the shape of a truncated rotating cone, which stands on a smaller base. The tank's volume is 465 m3, the radii of the bases are 4 m and 3 m. Find the depth of the tank.
  • The surface
    truncated_cone 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.
  • The truncated
    truncated_cone 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?
  • Truncated pyramid
    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 content. Calculate the area of the upper base.
  • Truncated pyramid
    truncated_pyramid Find the volume and surface area of a regular quadrilateral truncated pyramid if base lengths a1 = 17 cm, a2 = 5 cm, height v = 8 cm.
  • Truncated pyramid
    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 cone
    zrezany_kuzel Find the volume and surface area of the truncated cone if r1 = 12 cm, r2 = 5 cm and side s = 10 cm.
  • Wooden bowls
    miska 20 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 a d
  • Two vases
    komolykuzel 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 with the diameter of the upper base d2 = 15 cm. Which vas
  • Digging a pit
    komoly_jehlan 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. Determine how many m3 of soil were excavated when digging the pit?
  • Truncated pyramid
    komoly_jehlan The concrete pedestal in the shape of 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.
  • Truncated cone 6
    frustum-of-a-right-circular-cone Calculate the volume of the truncated cone whose bases consist of an inscribed circle and a circle circumscribed to the opposite sides of the cube with the edge length a=1.
  • Equilateral cone
    kuzel_rs We pour so much water into a container that has the shape of an equilateral cone, the base of which has a radius r = 6 cm, that one-third of the volume of the cone is filled. How high will the water reach if we turn the cone upside down?
  • Cutting cone
    kuzel_zrezany 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.
  • Runcated pyramid teapot
    komoly_jehlan 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 with the edges of the rectangular base b: 20 cm and c: 30 cm. How many liters of water will fit in the teapot?
  • Heptagonal pyramid
    truncated_hexagonal_pyramid A hardwood for a column is in the form of a frustum of a regular heptagonal pyramid. The lower base edge is 18 cm, and the upper base of 14 cm. The altitude is 30 cm. Determine the weight in kg if the wood density is 10 grams/cm3.
  • A concrete pedestal
    frustum-of-a-right-circular-cone A concrete pedestal has a shape of a right circular cone having a height of 2.5 feet. The diameter of the upper and lower bases are 3 feet and 5 feet, respectively. Determine the lateral surface area, total surface area, and the volume of the pedestal.
  • Frustum of a cone
    cone-frustrum A reservoir contains 28.54 m3 of water when full. The diameter of the upper base is 3.5 m, while at 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.

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