Top-open tank

The top-open tank has the shape of a truncated rotating cone, which stands on a smaller base. The tank's volume is 465 m³, the radii of the bases are 4 m and 3 m. Find the depth of the tank.

Correct answer:

h =  12 m

Step-by-step explanation:

$$\begin{gathered} r_1=4\text{ m } \\ {r}_2=3\text{ m } \\ V=465{\text{m}}^3 \\ V={\displaystyle \frac{1}{3}}\pi h(r_1^2+r_1{r}_2+r_2^2) \\ h={\displaystyle \frac{3\cdot V}{\pi \cdot (r_1^2+r_1\cdot r_2+r_2^2)}}={\displaystyle \frac{3\cdot 465}{3.1416\cdot (4^2+4\cdot 3+3^2)}}=12\text{ m} \end{gathered}$$

Try another example

Related math problems and questions:

• The truncated
  The truncated rotating cone has bases with radii r1 = 8 cm, r2 = 4 cm and height v = 5 cm. What is the volume of the cone from which the truncated cone originated?
• Truncated cone 3
  The surface of the truncated rotating cone S = 7697 meters square, the substructure diameter is 56m and 42m, find the height of the tang.
• Truncated cone
  Calculate the height of the rotating truncated cone with volume V = 794 cm³ and a base radii r₁ = 9.9 cm and r₂ = 9.8 cm.
• Frustrum - volume, area
  Calculate the surface and volume of a truncated rotating cone with base radii of 8 cm and 4 cm, height 5 cm.
• Truncated cone 6
  Calculate the volume of the truncated cone whose bases consist of an inscribed circle and a circle circumscribed to the opposite sides of the cube with the edge length a=1.
• 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.
• Frustum of a cone
  A reservoir contains 28.54 m³ of water when full. The diameter of the upper base is 3.5 m, while at the lower base is 2.5 m. Find the height if the reservoir is in the form of a frustum of a right circular cone.
• The surface
  The surface of a truncated rotating cone with side s = 13 cm is S = 510π cm². Find the radii of the bases when their difference in lengths is 10cm.
• Truncated pyramid
  How many cubic meters is the volume of a regular four-sided truncated pyramid with edges one meter and 60 cm and high 250 mm?
• 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.
• Digging a pit
  The pit has the shape of a regular quadrilateral truncated pyramid. The edges of the bases are 14m and 10m long. The sidewalls form an angle of 135° with a smaller base. Determine how many m³ of soil were excavated when digging the pit?
• 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?
• 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.
• Slant height
  The cone's slant height is 5cm, and the radius of its base is 3cm, find the volume of the cone.
• Truncated cone
  A truncated cone has bases with radiuses of 40 cm and 10 cm and a height of 25 cm. Calculate its surface area and volume.
• Cuboid edges
  The lengths of the cuboid edges are in the ratio 2: 3: 4. Find their length if you know that the surface of the cuboid is 468 m².
• Prism bases
  Volume perpendicular quadrilateral prism is 360 cm³. The edges of the base and height of the prism are in the ratio 5:4:2. Determine the area of the base and walls of the prism.