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.

Correct answer:

S₁ =  6050.84 cm²
S₂ =  8471.17 cm²

Step-by-step explanation:

$$\begin{gathered} v=43 \\ {S}_1=\pi r^2 \\ {S}_2=\pi rs \\ {S}_1:S_2=5:7=5\mathrm{/}7 \\ {\displaystyle \frac{\pi r^2}{\pi rs}}=5\mathrm{/}7 \\ r\mathrm{/}s=5\mathrm{/}7 \\ s=r\cdot 7\mathrm{/}5 \\ {s}^2=v^2+r^2 \\ {r}^2\cdot 7^2\mathrm{/}{5}^2=43^2+r^2 \\ {r}^2={\displaystyle \frac{1849}{1.96-1}} \\ {r}^2=1926.042 \\ r=\sqrt{1926.042}=43.89cm \\ s=r\cdot 7\mathrm{/}5=61.44cm \\ {S}_1=\pi r^2=\pi 43.89^2=6050.84{\text{cm}}^2 \end{gathered}$$

$S_2=\pi rs=\pi \cdot 43.89\cdot 61.44=8471.17{\text{cm}}^2$

Try another example

Related math problems and questions:

• 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.
• Area of the cone
  Calculate the surface area of the cone, you know the base diameter 25 cm and a height 40 cm.
• Surface of the cone
  Calculate the surface of the cone if its height is 8 cm and the volume is 301.44 cm³.
• 3sides prism
  The base of vertical prism is an isosceles triangle whose base is 10 cm and the arm is 13 cm long. Prism height is three times the height of base triangle. Calculate the surface area of the prism.
• 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 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.
• Rotating cone II
  Calculate area of surface of rotating cone with base radius r=19 cm and height h=9 cm.
• Cap
  Jesters hat is shaped by a rotating cone. Calculate how much paper is needed to the cap 54 cm high when the head circumference is 47 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
• 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 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
• 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.
• Lamp cone
  Calculate the surface of a lampshade shaped of a rotary truncated cone with a base diameter of 32 cm and 12 cm and height of 24 cm.
• 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.
• 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.
• Quadrilateral pyramid
  Calculate the surface of a quadrilateral pyramid, which has a rectangular base with dimensions a = 8 cm, b = 6 cm and height H = 10 cm.
• Frustrum - volume, area
  Calculate the surface and volume of the truncated cone, the radius of the smaller figure is 4 cm, the height of the cone is 4 cm and the side of the truncated cone is 5 cm.