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.

Correct answer:

V =  342.0868 cm³

Step-by-step explanation:

$$\begin{gathered} S_1=78.5{\text{cm}}^2 \\ {S}_2=219.8{\text{cm}}^2 \\ {S}_1=\pi r^2 \\ r=\sqrt{S_1\mathrm{/}\pi }=\sqrt{78.5\mathrm{/}3.1416}\doteq 4.9987\text{ cm } \\ {S}_2=\pi rs \\ s=S_2\mathrm{/}(\pi \cdot r)=219.8\mathrm{/}(3.1416\cdot 4.9987)\doteq 13.9965\text{ cm } \\ {s}^2=r^2+h^2 \\ h=\sqrt{s^2-r^2}=\sqrt{13.9965^2-4.9987^2}\doteq 13.0734\text{ cm } \\ V={\displaystyle \frac{1}{3}}\cdot S_1\cdot h={\displaystyle \frac{1}{3}}\cdot 78.5\cdot 13.0734=342.0868{\text{cm}}^3 \end{gathered}$$

Try another example

Related math problems and questions:

• Surface of the cone
  Calculate the surface of the cone if its height is 8 cm and the volume is 301.44 cm³.
• Cone A2V
  The surface of the cone in the plane is a circular arc with central angle of 126° and area 415 cm². Calculate the volume of a cone.
• 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.
• 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.
• 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.
• 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?
• The cone - S,V
  Calculate the volume and surface area of the cone if its radius r = 6 cm and side s = 10 cm.
• Triangular prism
  The base of the perpendicular triangular prism is a right triangle with a leg length of 5 cm. The content area of the largest sidewall of its surface is 130 cm², and the height of the body is 10 cm. Calculate its volume.
• Regular quadrilateral pyramid
  What is the volume of a regular quadrilateral pyramid if its surface is 576 cm² and the base edge is 16 cm?
• Circle sector
  Circular sector with a central angle 160° has area 452 cm². Calculate its radius r.
• Slant height
  The cone's slant height is 5cm, and the radius of its base is 3cm, find the volume of the cone.
• Quadrangular prism
  Calculate the volume and surface area of a regular quadrangular prism 35 cm high and the base diagonal of 22 cm.
• 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
• Truncated pyramid
  Find the volume and surface area of a regular quadrilateral truncated pyramid if base lengths a1 = 17 cm, a2 = 5 cm, height v = 8 cm.
• Cone and the ratio
  The rotational cone has a height 43 cm, and the ratio of the base surface to lateral surface is 5: 7. Calculate the surface of the base and the lateral surface.
• Calculate
  Calculate the cone's surface and volume that results from the rotation of the right triangle ABC with the squares 6 cm and 9 cm long around the shorter squeegee.
• Triangular pyramid
  It is given perpendicular regular triangular pyramid: base side a = 5 cm, height v = 8 cm, volume V = 28.8 cm³. What is it content (surface area)?