Rotating cone

The rotating cone has a base diameter of 18 dm and a height of 12 dm. Calculate the volume V.

Correct answer:

V =  1017.876 dm³

Step-by-step explanation:

$$\begin{gathered} D=18\text{ dm } \\ h=12\text{ dm } \\ r=D\mathrm{/}2=18\mathrm{/}2=9\text{ dm } \\ S=\pi \cdot r^2=3.1416\cdot 9^2\doteq 254.469{\text{dm}}^2 \\ V={\displaystyle \frac{1}{3}}\cdot S\cdot h={\displaystyle \frac{1}{3}}\cdot 254.469\cdot 12=1017.876{\text{dm}}^3 \end{gathered}$$

Try another example

Related math problems and questions:

• 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.
• Rotating cone
  Calculate volume of a rotating cone with base radius r=12 cm and height h=7 cm.
• The rotating
  The rotating cone has a height of 0.9 m and the diameter of the base is 7.2 dm. Calculate the surface of the cone. (Hint: use Pythagorean theorem for a side of cone)
• 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.
• Volume of cone
  Find the volume of a right circular cone-shaped building with a height of 9 m and a radius base of 7 m.
• Cone
  Circular cone with height h = 29 dm and base radius r = 3 dm slice plane parallel to the base. Calculate the distance of the cone vertex from this plane, if solids have the same volume.
• 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.
• The diagram
  The diagram is a cone of radius 8cm and height 10cm. The diameter of the base is. ..
• The base 2
  The base diameter of a right cone is 16cm and it's slant height is 12cm. A. ) Find the perpendicular height of the cone to 1 decimal place. B. ) Find the volume of the cone, convert to 3 significant figure. Take pi =3.14
• Rotating cone II
  Calculate area of surface of rotating cone with base radius r=19 cm and height h=9 cm.
• Height of the cylinder
  The cylinder volume is 150 dm cubic, the base diameter is 100 cm. What is the height of the cylinder?
• Cylinder
  Calculate the dimensions of rotating cylindrical containers with volume 2 l if the container's height is equal to the base's diameter.
• Surface and volume
  Calculate the surface and volume of a cylinder whose height is 8 dm and the radius of the base circle is 2 dm  
• 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
• Volume ratio
  Calculate the volume ratio of balls circumscribed (diameter r) and inscribed (diameter ϱ) into an equilateral rotating cone.
• Perimeter of base
  The circumference of the base of the rotating cylinder is same as its height. What is the diameter and height of this cylinder with volume 1 liter?
• The volume
  The volume of the cone is 94.2dm³, the radius of the base is 6 dm Calculate the surface of the cone.