Slant height

The cone's slant height is 5cm, and the radius of its base is 3cm, find the volume of the cone.

Correct answer:

V =  37.6991 cm³

Step-by-step explanation:

$$\begin{gathered} s=5\text{ cm } \\ r=3\text{ cm } \\ h=\sqrt{s^2-r^2}=\sqrt{5^2-3^2}=4\text{ cm } \\ {S}_1=\pi \cdot r^2=3.1416\cdot 3^2\doteq 28.2743{\text{cm}}^2 \\ V={\displaystyle \frac{1}{3}}\cdot S_1\cdot h={\displaystyle \frac{1}{3}}\cdot 28.2743\cdot 4=37.6991{\text{cm}}^3 \end{gathered}$$

Try calculation via our triangle calculator.

Try another example

Related math problems and questions:

• 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
• 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 pie =3.14
• Surface of the cone
  Calculate the surface of the cone if its height is 8 cm and the volume is 301.44 cm³.
• Cutting cone
  A cone with a base radius of 10 cm and a height of 12 cm is given. At what height above the base should we divide it by a section parallel to the base so that the volumes of the two resulting bodies are the same? Express the result in cm.
• Cone 15
  The radius of the base of a right circular cone is 14 inches and it's height 18 inches. What is the slant height?
• Rotating cone
  Find the rotating cone's surface and volume if its side is 150 mm long and the circumference of the base is 43.96 cm.
• Volume of the cone
  Calculate the volume of the cone if the content of its base is 78.5 cm² and the content of the shell is 219.8 cm².
• Pile of sand
  A large pile of sand has been dumped into a conical pile in a warehouse. The slant height of the pile is 20 feet. The diameter of the base of the sandpile is 31 feet. Find the volume of the pile of sand.
• The volume
  The volume of the cone is 94.2dm³, the radius of the base is 6 dm Calculate the surface of the cone.
• Cone
  Calculate the volume of the rotating cone with a base radius 26.3 cm and a side 38.4 cm long.
• Cone
  Circular cone of height 15 cm and volume 5699 cm³ is at one-third of the height (measured from the bottom) cut by a plane parallel to the base. Calculate the radius and circumference of the circular cut.
• 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.
• 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.
• 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.
• Rotary cone
  Rotary cone whose height is equal to the circumference of the base, has a volume 229 cm³. Calculate the radius of the base circle and height of the cone.
• Cone - from volume surface area
  The volume of the rotating cone is 1,018.87 dm³, and its height is 120 cm. What is the surface area of the cone?
• Axial cut
  The cone surface is 388.84 cm², the axial cut is an equilateral triangle. Find the cone volume.