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. - 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? - 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.
- 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. - Calculate the cone
The volume of the cone is 461.58 cm³. Its diameter is 14 cm. Calculate the surface area of this cone. - 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. - The volume
The volume of the rotating cone is 376.8cm³. The height of this cone is one dm. Calculate the diameter of the cone base.
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