Cone Problems

Number of problems found: 90

  • Volume of the cone
    kuzel2 Calculate the volume of the cone if the content of its base is 78.5 cm2 and the content of the shell is 219.8 cm2.
  • 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.
  • From plasticine
    kuzel_1 Michael modeled from plasticine a 15 cm high pyramid with a rectangular base with the sides of the base a = 12 cm and b = 8 cm. From this pyramid, Janka modeled a rotating cone with a base diameter d = 10 cm. How tall was Janka's cone?
  • 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.
  • Volume of the cone
    kuzel Find the volume of the cone with the base radius r and the height v. a) r = 6 cm, v = 8 cm b) r = 0,9 m, v = 2,3 m c) r = 1,4 dm, v = 30 dm
  • Storm and roof
    cone_church The roof on the building is a cone with a height of 3 meters and a radius equal to half the height of the roof. How many m2 of roof need to be repaired if 20% were damaged in a storm?
  • Surface and volume
    kuzel2_1 Find the surface and volume of the rotating cone if the circumference of its base is 62.8 m and the side is 25 m long.
  • How many
    strecha How many m2 of copper sheet is needed to replace the roof of a conical tower with a diameter of 13 meters and a height of 24 meters, if we count 8% of the material for bending and waste?
  • 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.
  • The conical
    cone_1 The conical candle has a base diameter of 20 cm and a side of 30 cm. How much dm ^ 3 of wax was needed to make it?
  • The funnel
    kuzel_rs The funnel has the shape of an equilateral cone. Calculate the content of the area wetted with water if you pour 3 liters of water into the funnel.
  • Volume ratio
    inside_cone Calculate the volume ratio of balls circumscribed (diameter r) and inscribed (diameter ϱ) into an equilateral rotating cone.
  • Surface of the cone
    kuzel3 Calculate the surface of the cone if its height is 8 cm and the volume is 301.44 cm3.
  • 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?
  • Calculate
    kuzel3 Calculate the surface and volume of the cone that results from the rotation of the right triangle ABC with the squares 6 cm and 9 cm long around the shorter squeegee.
  • The diagram 2
    cone The diagram shows a cone with slant height 10.5cm. If the curved surface area of the cone is 115.5 cm2. Calculate correct to 3 significant figures: *Base Radius *Height *Volume of the cone
  • Cone roof
    kuzel2 How many m2 of roofing is needed to cover a cone-shaped roof with a diameter of 10 m and a height of 4 m? Add an extra 4% to the overlays.
  • Lampshade
    kuzel_2 The cone-shaped lampshade has a diameter of 30 cm and a height of 10 cm. How many cm2 of material will we need when we 10% is waste?
  • Pile of sand
    pile_sand A large pile of sand has been dumped into a conical pile in a warehouse. The slant height of the pile is 20 feet. The diameter of the base of the sand pile is 31 feet. Find the volume of the pile of sand.
  • Sphere in cone
    sphere_in_cone A sphere is inscribed in the cone (the intersection of their boundaries consists of a circle and one point). The ratio of the surface of the ball and the contents of the base is 4: 3. A plane passing through the axis of a cone cuts the cone in an isoscele

Do you have an interesting mathematical word problem that you can't solve it? Submit a math problem, and we can try to solve it.

We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...