Practice problems of the cone
Number of problems found: 124
- Sphere submerged in the cone
A right circular cone with a top width of 24 cm and an altitude of 8 cm is filled with water. A spherical steel ball with a radius of 3.0cm is submerged in the cone. Find the volume of water below the sphere.
- Frustrum - volume, area
Calculate the surface and volume of a truncated rotating cone with base radii of 8 cm and 4 cm, height 5 cm.
- The diameter
The diameter of the cone is 24 cm, the radius is 12 cm. How many cm does height measure if it is one-third larger than the radius of the 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.
- The volume
The volume of the rotating cone is 376.8cm³, the height of this cone is 1dm. Calculate the diameter of the cone base.
- Hard cone problem
The surface of the cone is 200 cm², its height is 7 centimeters. Calculate the volume of this cone.
- Wooden bowls
20 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 a d
- Volume ratio
Calculate the volume ratio of balls circumscribed (diameter r) and inscribed (diameter ϱ) into an equilateral rotating cone.
- 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?
- Cone from cube
From a wooden block, 20 cm high was the turned largest possible cone. Calculate its weight if you know that the density of wood was 850 kg/m3
- Rotating cone
The rotating cone has a base diameter of 18 dm and a height of 12 dm. Calculate the volume V.
- 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
- Frustum of a cone
A reservoir contains 28.54 m³ of water when full. The diameter of the upper base is 3.5 m, while at 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.
- Castle model
The castle model has a cone-shaped roof. The cone side is 45 cm long and the base radius is 27 cm. a) What is the roof volume? b) How many dm² of wallpaper is used to glue the roof, ie the cone shell? c) What is the weight of the roof if it is made of woo
- The diagram
The diagram is a cone of radius 8cm and height 10cm. The diameter of the base is. ..
- Cone area and side
Calculate the surface area and volume of a rotating cone with a height of 1.25 dm and 17,8dm side.
- Gravel - cone
The mound of gravel has a regular circular cone shape with a height 3.3 meter and a base circumference of 18.85 meters. How many cubic meters of gravel is in a pile? Calculate the weight of gravel if its density is p = 640 kg / cubic m.
The radii of two cones are in the ratio 5.7 Calculate the area ratio if cones have same height.
- Surface area
The volume of a cone is 1000 cm³ and the content area of the axis cut is 100 cm². Calculate the surface area of the cone.
- Max - cone
From the iron bar (shape = prism) with dimensions 6.2 cm, 10 cm, 6.2 cm must be produced the greatest cone. a) Calculate cone volume. b) Calculate the waste.