Number of problems found: 90
- Volume of the cone
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
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
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
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
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
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
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
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
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
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
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
Calculate the volume ratio of balls circumscribed (diameter r) and inscribed (diameter ϱ) into an equilateral rotating cone.
- Surface of the cone
Calculate the surface of the cone if its height is 8 cm and the volume is 301.44 cm3.
- 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?
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
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
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.
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
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
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