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.

Result

V =  27482.653 cm3
S =  38.17 dm2
m =  15.4 kg

Solution:

s=45 cm r=27 cm  h=s2r2=452272=36 cm  V=13 π r2 h=13 3.1416 272 3627482.652527482.653 cm3s=45 \ \text{cm} \ \\ r=27 \ \text{cm} \ \\ \ \\ h=\sqrt{ s^2 - r^2 }=\sqrt{ 45^2 - 27^2 }=36 \ \text{cm} \ \\ \ \\ V=\dfrac{ 1 }{ 3 } \cdot \ \pi \cdot \ r^2 \cdot \ h=\dfrac{ 1 }{ 3 } \cdot \ 3.1416 \cdot \ 27^2 \cdot \ 36 \doteq 27482.6525 \doteq 27482.653 \ \text{cm}^3
S1=π r s=3.1416 27 453817.0351 cm2 S=S1dm2=S1/100 dm2=38.17035 dm2=38.17 dm2S_{1}=\pi \cdot \ r \cdot \ s=3.1416 \cdot \ 27 \cdot \ 45 \doteq 3817.0351 \ \text{cm}^2 \ \\ S=S_{1} \rightarrow dm^2=S_{1} / 100 \ dm^2=38.17035 \ dm^2=38.17 \ \text{dm}^2
ρ=0.56 g/cm3 m1=ρ V=0.56 27482.652515390.2857 g  m=m1kg=m1/1000 kg=15.39029 kg=15.4 kgρ=0.56 \ \text{g/cm}^3 \ \\ m_{1}=ρ \cdot \ V=0.56 \cdot \ 27482.6525 \doteq 15390.2857 \ \text{g} \ \\ \ \\ m=m_{1} \rightarrow kg=m_{1} / 1000 \ kg=15.39029 \ kg=15.4 \ \text{kg}



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