# Frustum Problems

#### Number of problems found: 24

- 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 14m and 10m long. The sidewalls form an angle of 135° with a smaller base. Determine how many m^{3}of soil were excavated when digging the pit? - Truncated pyramid

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. - Wooden bowls

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 cm^{2}. 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 - Frustum of a cone

A reservoir contains 28.54 m^{3}of water when completely full. The diameter of the upper base is 3.5 m while at the lower base is 2.5 m. Determine the height if the reservoir is in the form of a frustum of a right circular cone. - Truncated cone 6

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

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? - A concrete pedestal

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. - Truncated cone 5

The height of a cone 7 cm and the length of side is 10 cm and the lower radius is 3cm. What could the possible answer for the upper radius of truncated cone? - Heptagonal 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 density of the wood is 10 grams/cm^{3}. - 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 diameter of the lower base d1 = 25 cm and with the diameter of the upper base d2 = - 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 with the edges of the rectangular base b: 20 cm and c: 30 cm. How many liters of water will fit in the teapot? - Truncated cone

Calculate the height of the rotating truncated cone with volume V = 1115 cm^{3}and a base radii r_{1}= 7.9 cm and r_{2}= 9.7 cm. - Truncated cone

A truncated cone has a bases radiuses 40 cm and 10 cm and a height of 25 cm. Calculate its surface area and volume. - Hexagon cut pyramid

Calculate the volume of a regular 6-sided cut pyramid if the bottom edge is 30 cm, the top edge us 12 cm, and the side edge length is 41 cm. - Truncated cone 3

The surface of the truncated rotating cone S = 7697 meters square, the substructure diameter is 56m and 42m, determine the height of the tang. - Lamp cone

Calculate the surface of a lamp shade shaped of a rotary truncated cone with base diameter 32 cm and 12 cm and height 24 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 side wall and the plane of the base.) S =? , V =? - Truncated pyramid

How many cubic meters is volume of a regular four-side truncated pyramid with edges one meter and 60 cm and high 250 mm? - Pillar

Calculate volume of pillar shape of a regular tetrahedral truncated pyramid, if his square have sides a = 19, b = 27 and height is h = 48.

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