Question #111968
1. A lampshade is in the form of a frustum of a cone of which the top and the bottom diameters are 20cm and 30cm respectively, and the vertical height is 12cm.
Calculate:
a. the area of material required to cover the lampshade
b. What is the volume of the lampshade?
1
Expert's answer
2020-04-24T20:51:39-0400

r=10cm,R=15cm,h=12cmr=10 cm, R=15cm, h=12 cm

a.

S=πl(R+r),S=\pi l(R+r), where l=h2+(Rr)2.l=\sqrt{h^2+(R-r)^2}.

l=122+(1510)2=169=13.l=\sqrt{12^2+(15-10)^2}=\sqrt{169}=13.

S=π13(15+10)=325πcm2.S=\pi 13(15+10)=325\pi cm^2.


b. V=13πh(R2+Rr+R2)=13π12(152+1510+102)=V=\frac{1}{3}\pi h(R^2+Rr+R^2)=\frac{1}{3}\pi 12(15^2+15*10+10^2)=

=4π(225+150+100)=1900πcm3.=4\pi(225+150+100)=1900\pi cm^3.


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