Surface of the cone

Calculate the surface of the cone if its height is 8 cm and the volume is 301.44 cm³.

Correct result:

S =  301.4706 cm²

Solution:

$$\begin{gathered} h=8\text{ cm } \\ V=301.44{\text{cm}}^3 \\ V={\displaystyle \frac{1}{3}}\cdot S_1\cdot h \\ {S}_1={\displaystyle \frac{3\cdot V}{h}}={\displaystyle \frac{3\cdot 301.44}{8}}={\displaystyle \frac{2826}{25}}=113.04{\text{cm}}^2 \\ {S}_1=\pi r^2 \\ r=\sqrt{S_1\mathrm{/}\pi }=\sqrt{113.04\mathrm{/}3.1416}\doteq 5.9985\text{ cm } \\ s=\sqrt{r^2+h^2}=\sqrt{5.9985^2+8^2}\doteq 9.9991\text{ cm } \\ {S}_2=\pi \cdot r\cdot s=3.1416\cdot 5.9985\cdot 9.9991\doteq 188.4306{\text{cm}}^2 \\ S=S_1+S_2=113.04+188.4306=301.4706{\text{cm}}^2 \end{gathered}$$

Try another example

Showing 0 comments:

Related math problems and questions:

• Cone - from volume surface area
  The volume of the rotating cone is 1,018.87 dm³, its height is 120 cm. What is the surface area of the cone?
• 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.
• 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.
• 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.
• Slant height
  The cone's slant height is 5cm, and the radius of its base is 3cm, find the volume of the cone.
• Rotating cone
  Find the surface and volume of the rotating cone if its side is 150 mm long and the circumference of the base is 43.96 cm.
• Calculate
  Calculate the surface and volume of the cone that results from the rotation of the right triangle ABC with the squares 6 cm and 9 cm long around the shorter squeegee.
• Cone - side
  Find the surface area and volume of the cone if its height is 125 mm and the side length is 17 cm.
• The cone - S,V
  Calculate the volume and surface area of the cone if its radius r = 6 cm and side s = 10 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
• 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.
• Find the
  Find the surface area of a regular quadrilateral pyramid which has a volume of 24 dm³ and a height of 45 cm.
• Cone and the ratio
  Rotational cone has a height 23 cm and the ratio of the base surface to lateral surface is 7: 9. Calculate a surface of the base and the lateral surface.
• Base of prism
  The base of the perpendicular prism is a rectangular triangle whose legs length are at a 3: 4 ratio. The height of the prism is 2cm smaller than the larger base leg. Determine the volume of the prism if its surface is 468 cm².
• Truncated cone
  Find the volume and surface area of the truncated cone if r1 = 12 cm, r2 = 5 cm and side s = 10 cm.
• 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.
• 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.