If a right circular cone is radius 4 cm and slant height 5 cm then what is its volume?
Answers
Solution :-
Here,
A right circular cone is given
Radius of right circular cone = 4 cm
Slant height of right circular cone = 5cm
Let the height of the cone be h
Therefore,
l^2 = r^2 + h^2
Subsitute the required values,
( 5 )^2 = ( 4 )^2 + h^2
25 = 16 + h^2
h^2 = 25 - 16
h^2 = 9
h = √ 9
h = √ 3 * 3
h = 3
Thus, The height of the right circular cone is 3cm
Now,
We have to find the volume of cone
As we know that,
Volume of cone = 1/3 πr^2h
Volume of cone
= 1/3 * 22/7 * 4 * 4 *3
= 1/3 * 22/7 * 16 * 3
= 22/7 * 16
= 352/7
= 50.28cm^3
Hence, the volume of the right circular cone is 50.28cm^3 
Step-by-step explanation:
Given:-
right circular cone is radius 4 cm and slant height 5 cm
To find:-
Find the volume of the cone?
Solution:-
Radius of the given cone (r)=4cm
Slant height of the cone (l)=5 cm
we know that
if the radius of the cone is 'r' units and height is 'h' units then slant height of the cone is √{h^2+r^2 } units
Let height of the cone be 'h' units
=>5= √[h^2+4^2]
= 5= [√h^2+16]
On squaring both sides then
=>(5)^2 = [√h^2+16]^2
=>25= h^2+16
=>h^2 = 25-16
=>h^2 = 9
=>h=±√9
=>h=±3
Since the value of h cannot be negative
h=3 cm
Height of the circular cone = 3 cm
Volume of a cone = (1/3)πr^2h cubic units
=>V=(1/3)×(22/7)×(4)^2(3) cubic cm
=>V = (22/21)×16×3
=>V= (22×16×3)/21
=>V=22×16/7
=>V=352/7
=>V=50.2857...
=>V=50.29 cubic cm
(correct it two decimals)
Answer:-
The volume of the given circular cone = 50.29 cubic cm
Used formulae:-
- the radius of the cone is 'r' units and height is 'h' units then slant height of the cone is √{h^2+r^2 } units
- Volume of a cone = (1/3)πr^2h cubic units