Question #148932
8. A right circular cylinder with an altitude of 40 cm and base diameter of 30cm has a right circular cone at its top with the same base. If the cone is 60cm high, determine its lateral area in cm2.
1
Expert's answer
2020-12-13T18:43:36-0500

Solution. The lateral area of the body is equal to the sum of the lateral area of the right circular cylinder and the lateral area of the right circular cone


S=Scylinder+SconeS=S_{cylinder}+S_{cone}

The lateral area of the right circular cylinder


Scylinder=π×dH1S_{cylinder}=\pi\times dH_1

where d=30cm is base diameter; H1=40cm is altitude of the right circular cylinder.


Scylinder=π×30×40=1200πcm2S_{cylinder}=\pi\times 30\times 40=1200\pi cm^2

The lateral area of the right circular cone

Scone=π×rLS_{cone}=\pi\times rL

where r=d/2=15cm is cone base radius, L is slant height of the cone.


L=r2+h2=152+602=3825=5153L=\sqrt{r^2+h^2}=\sqrt{15^2+60^2}=\sqrt{3825}=5\sqrt{153}

where h=60cm is high oh the right circular cone.


Scone=π×15×5153=75π153cm2S_{cone}=\pi\times 15\times 5\sqrt{153}=75\pi\sqrt{153} cm^2

As result


S=1200π+75π1536684cm2S=1200\pi+75\pi\sqrt{153} \approx 6684 cm^2

Answer.

S=1200π+75π1536684cm2S=1200\pi+75\pi\sqrt{153} \approx 6684 cm^2


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