The base tadious and height of a cone is 5cm and 25cm respectively. If the condition is cut parallel to its base at a height of h from the base. If the volume of this frustum 110cm cube. find the radius of the smaller cone
Answers
Answer: The radius of smaller cone would be 4.7 cm.
Step-by-step explanation:
Dimensions of bigger cone is given by:
R= 5cm
H= 25cm
Dimension of smaller cone would be:
Radius= r
Height= 25-h
We know both the cones are similar, so the ratio of corresponding sides would be equal.
r/R=(25-h)/H
25-h=r*H/R=r*25/5=5r
So,
The volume of the frustum= volume of bigger cube - volume of smaller cube= 1/3*pi*(R^2*H-r^2(25-h))
110= 1/3*22/7*(5^2*25-r^2*5r)
105= 625-5r^3
5r^3=625-105=520
r^3=104
Taking cube root, we get
r= 4.7cm
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Answer:
Step-by-step explanation:
Volume of cone=(πr^2h)/3
=22/7*5*5*25
=22/7*625
=1964.28cubic cm
Volume of smaller cone= Total volume of cone-Volume of frustum
Volume of smaller cone=1964.28-110
=1854.28cubic cm