Given,
Slant height of right circular cone ( l 1 ) = 9 f t (l_1)=9ft ( l 1 ) = 9 f t
Base radius ( r 1 ) = 5 f t (r_1)= 5ft ( r 1 ) = 5 f t
and ( r 2 ) = 7 f t (r_2)=7ft ( r 2 ) = 7 f t
a) Lateral area of the frustum = π ( r 2 − r 1 ) l 1 =\pi (r_2-r_1)l_1 = π ( r 2 − r 1 ) l 1
= 3.14 ( 7 − 5 ) × 9 = 3.14 × 2 × 9 = 59.52 f t 2 =3.14 (7-5)\times 9 \\
=3.14\times 2\times 9 \\
=59.52ft^2 = 3.14 ( 7 − 5 ) × 9 = 3.14 × 2 × 9 = 59.52 f t 2
b) Altitude of the frustum
h ′ = ( 9 2 − 4 2 ) = 77 = 8.87 f t h'=(\sqrt{9^2-4^2})=\sqrt{77}=8.87ft h ′ = ( 9 2 − 4 2 ) = 77 = 8.87 f t
cos ( θ ) = r 2 − r 1 l 1 = 7 − 2 9 = 2 9 ⇒ θ = cos − 1 ( 2 9 ) ⇒ θ = 77.1 6 ∘ \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 cos ( θ ) = l 1 r 2 − r 1 = 9 7 − 2 = 9 2 ⇒ θ = cos − 1 ( 9 2 ) ⇒ θ = 77.1 6 ∘
c) Altitude of the cone complete cone
So, tan ( θ ) = h 7 \tan(\theta)=\frac{h}{7} tan ( θ ) = 7 h
h = tan ( 77.16 ) × 7 = 30.7 f t h=\tan(77.16)\times 7 = 30.7ft h = tan ( 77.16 ) × 7 = 30.7 f t
Comments