Practice problems of the cone - page 10 of 12
Number of problems found: 229
- 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. (Cone side is the segment joining the vertex cone with any point of the base circle. All sides of - 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. - 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? - 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. - 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. - Surface 64744
The cone is 12 cm high, and the radius of the figure is 9 cm. Find out its surface. - 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? - 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. - Sphere
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. - Determine 73454
The volume of the cut cone is V = 38000π cm³. The radius of the lower base is 10 cm larger than the radius of the upper base. Determine the radius of the base if height v = 60 cm. - 2x cone
Circular cone height 84 cm was cut plane parallel with the base. The volume of these two small cones is the same. Calculate the height of the smaller cone. - The surface
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. - Determine 4876
The rotating cone has a height of 72 cm and an angle at the top of 72 °. Determine the volume of the sphere. - 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 lower base d1 = 25 cm and the diameter of the upper base d2 = 15 cm. Which vase can - Calculate 38701
Calculate the surface and volume of the cut rotating cone with base radii of 14cm and 8cm height of 11cm.
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