Question #275136

3. Given a frustum of a right circular cone with a slant height of 9ft ., and the radii of bases are 5ft and 7ft. Find:







a. The lateral area







b. Altitude of the frustum







c. The altitude of the entire cone if the cone removed was replaced








1
Expert's answer
2021-12-07T09:36:03-0500

Given,

Slant height of right circular cone (l1)=9ft(l_1)=9ft

Base radius (r1)=5ft(r_1)= 5ft

and (r2)=7ft(r_2)=7ft

a) Lateral area of the frustum =π(r2r1)l1=\pi (r_2-r_1)l_1

=3.14(75)×9=3.14×2×9=59.52ft2=3.14 (7-5)\times 9 \\ =3.14\times 2\times 9 \\ =59.52ft^2

b) Altitude of the frustum

h=(9242)=77=8.87fth'=(\sqrt{9^2-4^2})=\sqrt{77}=8.87ft

cos(θ)=r2r1l1=729=29θ=cos1(29)θ=77.16\cos(\theta)=\frac{r_2-r_1}{l_1} \\ =\frac{7-2}{9} \\ =\frac{2}{9}\\ \Rightarrow \theta = \cos^{-1}(\frac{2}{9}) \\ \Rightarrow \theta = 77.16^\circ

c) Altitude of the cone complete cone

So, tan(θ)=h7\tan(\theta)=\frac{h}{7}

h=tan(77.16)×7=30.7fth=\tan(77.16)\times 7 = 30.7ft


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