Answer to Question #111968 in Geometry for onyi

Question

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?

Answer 1

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

a.

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

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

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

b. $V=\frac{1}{3}\pi h(R^2+Rr+R^2)=\frac{1}{3}\pi 12(15^2+15*10+10^2)=$

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