Castle model

The castle model has a cone-shaped roof. The cone side is 45 cm long and the base radius is 27 cm.
a) What is the roof volume?
b) How many dm2 of wallpaper is used to glue the roof, ie the cone shell?
c) What is the weight of the roof if it is made of wood with a density of 0.56 g/cm3?
  They were rounded to tenths of a kilogram.

Correct answer:

V =  27482.6525 cm3
S =  38.1704 dm2
m =  15.4 kg

Step-by-step explanation:

s=45 cm r=27 cm  h=s2r2=452272=36 cm  V=13 π r2 h=13 3.1416 272 36=27482.6525 cm3=2.748104 cm3
S1=π r s=3.1416 27 453817.0351 cm2 S=S1 dm2=S1/100  dm2=3817.0351/100  dm2=38.17 dm2=38.1704 dm2
ρ=0.56 g/cm3 m1=ρ V=0.56 27482.652515390.2854 g  m=m1 kg=m1/1000  kg=15390.2854/1000  kg=15.4 kg=15.4 kg



Did you find an error or inaccuracy? Feel free to write us. Thank you!



avatar




Tips to related online calculators
Do you know the volume and unit volume, and want to convert volume units?
Tip: Our Density units converter will help you with the conversion of density units.
Do you want to convert mass units?

You need to know the following knowledge to solve this word math problem:

Related math problems and questions:

  • School model
    jehlan_4b_obdelnik The beech school model of a regular quadrilateral pyramid has a base 20 cm long and 24 cm high. Calculate a) the surface of the pyramid in square decimeters, b) the mass of the pyramid in kilograms if the density of the beech is ρ = 0,8 g/cm ^ 3
  • Canopy
    cone-roof Mr Peter has a metal roof cone shape with a height of 127 cm and radius 130 cm over well. He needs to paint the roof with anticorrosion. How many kg of color must he buy if the manufacturer specifies the consumption of 1 kg to 3.3 m2?
  • Cuboid 5
    drevo Calculate the mass of the cuboid with dimensions of 12 cm; 0.8 dm and 100 mm made from spruce wood (density = 550 kg/m3).
  • Wooden bowls
    miska 20 wooden bowls in the shape of a truncated cone should be painted on the outside and inside with wood varnish. We need 0.1 l of paint to paint 200 cm2. How many liters of paint do we have to buy if the bowls are 25 cm high, the bottom of the bowl has a d
  • Cone from cube
    cones From a wooden block, 20 cm high was the turned largest possible cone. Calculate its weight if you know that the density of wood was 850 kg/m3
  • Wall thickness
    sphere_Nickel The hollow metal ball has an outside diameter of 40 cm. Determine the wall thickness if the weight is 25 kg and the metal density is 8.45 g/cm3.
  • Rotating cone
    kuzel Calculate the volume and the surface area of a rotating cone of base radius r = 2.3 dm and a height h = 46 mm.
  • Gravel - cone
    hromada The mound of gravel has a regular circular cone shape with a height 3.3 meter and a base circumference of 18.85 meters. How many cubic meters of gravel is in a pile? Calculate the weight of gravel if its density is p = 640 kg / cubic m.
  • The pipe
    roura The pipe is 1.5 m long. Its outer diameter is 60 cm, inner diameter is 52 cm. Calculate the pipe's weight if the material's density from which it is made is 2 g/cm3. Round the results to whole kilograms.
  • Cone - side
    cones Find the cone's surface area and volume if its height is 125 mm and the side length is 17 cm.
  • The square
    woord The square oak board (with density ρ = 700 kg/m3) has a side length of 50 cm and a thickness of 30 mm. 4 holes with a diameter of 40 mm are drilled into the board. What is the weight of the board?
  • Wood prisms
    wood How many weight 25 prisms with dimensions 8x8x200 cm? 1 cubic meter of wood weighs 800 kg.
  • Truncated cone
    komoly_kuzel 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.
  • Two vases
    komolykuzel 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
  • Copper plate
    plech Calculate the thickness of the copper plate with a density 8.7 g/cm³ measuring 1.5 meters and 80 cm and its weight is 3.65 kg
  • Area of the cone
    cone2 Calculate the surface area of the cone, you know the base diameter 25 cm and a height 40 cm.
  • Sphere
    1sphere The surface of the sphere is 12100 cm2, and the weight is 136 kg. What is its density?