From plasticine

Michael modeled from plasticine a 15 cm high pyramid with a rectangular base with the sides of the base a = 12 cm and b = 8 cm. From this pyramid, Janka modeled a rotating cone with a base diameter d = 10 cm. How tall was Janka's cone?

Correct answer:

h₂ =  18.3346 cm

Step-by-step explanation:

$$\begin{gathered} a=12\text{ cm } \\ b=8\text{ cm } \\ {h}_1=15\text{ cm } \\ d=10\text{ cm } \\ r=d\mathrm{/}2=10\mathrm{/}2=5\text{ cm } \\ {S}_1=a\cdot b=12\cdot 8=96{\text{cm}}^2 \\ {V}_1={\displaystyle \frac{1}{3}}\cdot S_1\cdot h_1={\displaystyle \frac{1}{3}}\cdot 96\cdot 15=480{\text{cm}}^3 \\ {V}_1=V_2 \\ {V}_2={\displaystyle \frac{1}{3}}\cdot \pi \cdot r^2\cdot h_2 \\ {h}_2={\displaystyle \frac{3\cdot V_1}{\pi \cdot r^2}}={\displaystyle \frac{3\cdot 480}{3.1416\cdot 5^2}}=18.3346\text{ cm} \end{gathered}$$

Try another example

Related math problems and questions:

• 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.
• Quadrilateral pyramid,
  A quadrilateral pyramid, which has a rectangular base with dimensions of 24 cm, 13 cm. The height of the pyramid is 18cm. Calculate 1/the area of the base 2/casing area 3/pyramid surface 4/volume of the pyramid
• A plasticine
  Jožko modeled from plasticine. He used 27g of plasticine to model a 3 cm long cube. How many grams of plasticine will it need to mold cubes with an edge of 6cm?
• The quadrilateral pyramid
  The quadrilateral pyramid has a rectangular base of 24 cm x 3.2dm and a body height of 0.4m. Calculate its volume and surface area.
• 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.
• The volume
  The volume of the rotating cone is 376.8cm³, the height of this cone is 1dm. Calculate the diameter of the cone base.
• Cone
  The rotating cone volume is 9.42 cm³, with a height 10 cm. What angle is between the side of the cone and its base?
• Quadrilateral pyramid
  We have a regular quadrilateral pyramid with a base edge a = 10 cm and a height v = 7 cm. Calculate 1/base content 2/casing content 3/pyramid surface 4/volume of the pyramid
• 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 pi =3.14
• 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?
• Quadrilateral pyramid
  In a regular quadrilateral pyramid, the height is 6.5 cm and the angle between the base and the side wall is 42°. Calculate the surface area and volume of the body. Round calculations to 1 decimal place.
• Tetrahedral pyramid
  It is given a regular tetrahedral pyramid with a base edge of 6 cm and the height of the pyramid 10 cm. Calculate the length of its side edges.
• 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.
• 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.
• Truncated pyramid
  The truncated regular quadrilateral pyramid has a volume of 74 cm³, a height v = 6 cm, and an area of the lower base 15 cm² greater than the upper base's content. Calculate the area of the upper base.
• Quadrilateral prism
  The height of a regular quadrilateral prism is v = 10 cm, the deviation of the body diagonal from the base is 60°. Determine the length of the base edges, the surface, and the volume of the prism.
• Two vases
  Michaela has two vases in her collection. The first vase has the shape of a cone with a base diameter d = 20 cm; the second vase has the shape of a truncated cone with the lower base d1 = 25 cm and with the diameter of the upper base d2 = 15 cm. Which vas