Cone practice problems - page 10 of 12
Number of problems found: 235
- Sphere in cone
A sphere of radius 3 cm describes a cone with minimum volume. Determine cone dimensions. - 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 ball's surface and the area of the base is 4:3. A plane passing through the axis of a cone cuts the cone in an isosceles triangle - Rotating cone
How does the volume of the rotating cone change if: a) double the radius of the base b) We reduce the height three times c) Reduce the radius of the base five times - 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
- Consumption 15663
The cone-shaped sheet metal roof has a base diameter of 80 cm and a height of 60 cm. If 1 kg of paint is consumed per 6 m² of sheet metal, calculate the paint consumption for painting this roof. - Confectionery 7318
The confectioner needs to carve a cone-shaped decoration from a ball-shaped confectionery mass with a radius of 25 cm. Find the radius of the base of the ornament a (and the height h). He uses as much material as possible is used to make the ornament. - Volume ratio
Calculate the volume ratio of balls circumscribed (diameter r) and inscribed (diameter ϱ) into an equilateral rotating cone. - The cone
The cone's lateral surface area is 4 cm², and the area of the base is 2 cm². Find the angle in degrees (deviation) of the cone sine and the cone base plane. (The cone side is the segment joining the vertex cone with any point of the base circle. All sides - Funnel
The funnel has the shape of an equilateral cone. Calculate the surface wetted with water if we poured into the funnel 7.1 liters of water.
- 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. - 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 of 10 cm. How tall was Janka's cone? - Cone
The rotating cone volume is 9.42 cm3, with a height of 10 cm. What angle is between the side of the cone and its base? - Equilateral 81222
A sphere is inscribed in an equilateral cone with a base diameter of 12 cm. Calculate the volume of both bodies. What percentage of the volume of the cone is filled by the inscribed sphere? - Martians
A sphere-shaped spaceship with a diameter of 6 m landed in the meadow. To avoid attracting attention, the Martians covered it with a roof in the shape of a regular cone. How high will this roof be so that the consumption of roofing is minimal?
- 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. - Sphere and cone
Within the sphere of radius G = 33 cm, inscribe the cone with the largest volume. What is that volume, and what are the dimensions of the cone? - Surface 64744
The cone is 12 cm high, and the radius of the figure is 9 cm. Find out its surface. - Statements true/false
Which of the statements is not correct: ... - One-quarter 46001
Express in square centimeters the surface of a sphere whose radius is equal to one-quarter of the radius of the cone. The diameter of the base of the cone is 20 cm.
Intersect between the plane and a sphere is a circle with a radius of 60 mm. The cone, whose base is this circle and whose apex is at the center of the sphere, has a height of 34 mm. Calculate the surface area and volume of a sphere.Do you have homework that you need help solving? Ask a question, and we will try to solve it. Solving math problems.
