# Cone + body volume - math problems

1. 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
2. Conical bottle When a conical bottle rests on its flat base, the water in the bottle is 8 cm from it vertex. When the same conical bottle is turned upside down, the water level is 2 cm from its base. What is the height of the bottle?
3. Axial section of the cone The axial section of the cone is an isosceles triangle in which the ratio of cone diameter to cone side is 2: 3. Calculate its volume if you know its area is 314 cm square.
4. Cone side Calculate the volume and area of the cone whose height is 10 cm and the axial section of the cone has an angle of 30 degrees between height and the cone side.
5. A concrete pedestal A concrete pedestal has a shape of a right circular cone having a height of 2.5 feet. The diameter of the upper and lower bases are 3 feet and 5 feet, respectively. Determine the lateral surface area, total surface area, and the volume of the pedestal.
6. Frustum of a cone A reservoir contains 28.54 m3 of water when completely full. The diameter of the upper base is 3.5 m while at the lower base is 2.5 m. Determine the height if the reservoir is in the form of a frustum of a right circular cone.
7. Right circular cone The volume of a right circular cone is 5 liters. Calculate the volume of the two parts into which the cone is divided by a plane parallel to the base, one-third of the way down from the vertex to the base.
8. Lateral surface area The ratio of the area of the base of the rotary cone to its lateral surface area is 3: 5. Calculate the surface and volume of the cone, if its height v = 4 cm.
9. The diagram 2 The diagram shows a cone with slant height 10.5cm. If the curved surface area of the cone is 115.5 cm2. Calculate correct to 3 significant figures: *Base Radius *Height *Volume of the cone
10. Slant height The slant height of cone is 5cm and the radius of its base is 3cm, find the volume of the cone
11. Volcano The crater of a volcano is approximately in the shape of a cone of a base 3.1416 sq. Mi. The crater's depth is 1500 ft. How many cubic yards of earth would be required to fill this cavity?
12. Volume of cone Find the volume of a right circular cone-shaped building with a height of 9 cm and a radius base of 7 cm.
13. Conical area A right angled triangle has sides a=12 and b=19 in right angle. The hypotenuse is c. If the triangle rotates on the c side as axis, find the volume and surface area of conical area created by this rotation.
14. Hexagon rotation A regular hexagon of side 6 cm is rotated through 60° along a line passing through its longest diagonal. What is the volume of the figure thus generated?
15. Cone Calculate the volume of the rotating cone with a base radius 26.3 cm and a side 38.4 cm long.
16. Rotary bodies The rotating cone and the rotary cylinder have the same volume 180 cm3 and the same height v = 15 cm. Which of these two bodies has a larger surface area?
17. Axial cut The cone surface is 388.84 cm2, the axial cut is an equilateral triangle. Find the cone volume.
18. Rotating cone Calculate the volume and the surface area of a rotating cone of base radius r = 2.3 dm and a height h = 46 mm.
19. 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.
20. Cone container Rotary cone-shaped container has a volume 1000 cubic cm and a height 12 cm. Calculate how much metal we need for making this package.

Do you have an interesting mathematical word problem that you can't solve it? Enter it, and we can try to solve it.

We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...