Answer:
Step-by-step explanation:
volume of cone=1/3 πr²h
volume of frustum=vol of larger cone-vol of smaller cone=1/3πR²H-1/3πr²h
=1/3π(R²H-r²h)
=1/3π(4.5²×9-3²×6)
=1/3π×9×3(4.5×1.5-2)
=9π(6.75-2)
=9π×4.75
=42.75π cm³
The volume of frustum of cone is [tex]42.75\pi[/tex]
Frustum of cone is the part of cone when it is cut by a plane into two parts. The upper part of cone remains same in shape but the bottom part makes a frustum. To get this part of the right circular cone we have to slice it horizontally or parallel to the base.
Volume of frustum of cone = [tex]\frac{\pi H}{3} [ R^{2} + r^{2} + rR][/tex]
Where,
R = Radius of the bigger circular end
r = radius of the smaller circular end
H = height of frustum
According to the question
Original height of cone = 9 cm
Radius of the bigger circular end = 4.5 cm
Radius of the smaller circular end = 3 cm
Height of frustum = 3 cm
Volume of frustum of cone = [tex]\frac{\pi H}{3} [ R^{2} + r^{2} + rR][/tex]
= [tex]\frac{\pi 3}{3} [ 4.5^{2} + 3^{2} + 4.5*3][/tex]
= [tex]\pi [ 20.25 + 9 + 13.5][/tex]
= [tex]42.75\pi[/tex]
Hence, The volume of frustum of cone is [tex]42.75\pi[/tex] .
To know more volume of frustum of cone here:
https://brainly.com/question/24383178
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