Cone practice problems
A cone is a geometric solid formed by rotating a right triangle around one of its legsMain parts and properties of a cone:
- Base – a circle that forms the bottom of the cone.
- Vertex – the highest point of the cone.
- Height (h) – the distance from the vertex of the cone to the base (perpendicular distance).
- Side of the cone (shell) – the curved surface that connects the vertex with the base.
- Diameter of the base, (d=2r) – the width of the base.
- Radius of the base (r) – half the diameter of the base.
Number of problems found: 245
- Spheres to cone
Two solid spheres of radii 2 cm and 4 cm are melted and recast into a cone of height 8 cm. Find the radius of the cone so formed. - An ice cream
An ice cream machine has 3 flavors - vanilla, chocolate, and strawberry. The ice cream can be served in 2 ways - in a cone or in a cup. Along with the ice cream, there are 5 options for toppings - hot fudge, caramel, nuts, cherries, and sprinkles. What is - Revolving to cone
A triangle whose sides are 20 cm, 16 cm, and 12 cm is revolving around its greatest side as axis. What is the volume space it generates after a full revolution in cubic centimeters? - A conical
A conical tent can accommodate 11 people. Each person needs 4 m² of space on the ground and 20 m³ of air to breathe. Find the height of the tent. - A cone 3
A cone has a diameter of x cm and a slant height of y cm. A square pyramid has a base side length of x cm and a slant height of y cm. Which has the greater surface area? Explain. - A cone 4
A cone with a radius of 10 cm is divided into two parts by drawing a plane through the midpoint of its axis parallel to its base. Compare the volumes of the two parts. - A lamp
A lamp shade like that of a frustum has a height of 12 cm and an upper and lower diameter of 10 cm and 20 cm. What area of materials is required to cover the curved surface of the frustum? - A solid
A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid . - Lamp shade
A lamp shade is in the form of a frustum of a cone with slant height 7 in., radii of bases 3 in. and 7 in. respectively. How much material is used in its construction if ¼ in. is allowed for the seam. - Slant height 3
The frustum of a right circular cone has the diameters of base 10 cm of top 6 cm and a height of 5 cm. Find the slant height. - Ratio
The radii of the two cones are in the ratio of 5.7. Calculate the area ratio of cones that have the same height. - The diagram
The diagram shows a cone radius of 8cm and a height of 10cm. How long is the diameter of the base? - Rotating cone
Calculate the volume of a rotating cone with base radius r=18 cm and height h=20 cm. - Calculate the cone
The volume of the cone is 461.58 cm³. Its diameter is 14 cm. Calculate the surface area of this cone. - The diameter
The cone's diameter is 24 cm, and the radius is 12 cm. How many cm does height measure if it is one-third larger than the radius of the cone? - Cone-shaped 43291
Calculate the volume and weight of a pile of cone-shaped sand with a diameter of 8m and a height of v = 4.5m; the density of sand is 1500kg/M cubic. - 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 - Hard cone problem The cone's surface is 200 cm², and its height is 7 centimeters. Calculate the volume of this cone.
- Cross-sections of a cone
Cone with base radius 15 cm and height 20 cm divided by parallel planes to base into three bodies. The planes divide the height of the cone into three equal parts. Determine the volume ratio of the maximum and minimum of the resulting body. - Circumference 27161
Sketch the cone mesh and add the side length, the arc length of the circle, and the circle length to it, if you know: the side length of the cone: s = 51.9 cm cone base circumference = O = 151 mm.
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