Asked by Josh
                The diameter of the base of the cone is 24x cm.
The height of the cone is 16x cm.
The curved surface area of the cone is 2160pi cm^2.
The volume of the cone is V pi cm^3, where V is an integer.
What is the value of V. Answer is cm^2.
Thanks a lot.
            
        The height of the cone is 16x cm.
The curved surface area of the cone is 2160pi cm^2.
The volume of the cone is V pi cm^3, where V is an integer.
What is the value of V. Answer is cm^2.
Thanks a lot.
Answers
                    Answered by
            Steve
            
    πr√(r^2+h^2) = 2160π
(12x)√(144x^2+256x^2) = 2160
(12x)(20x) = 2160
x^2 = 9
x = 3
so, the volume is
π/3 r^2h
= (π/3) (24*3)^2 (16*3)
= 82944π
V = 82944 cm^3
    
(12x)√(144x^2+256x^2) = 2160
(12x)(20x) = 2160
x^2 = 9
x = 3
so, the volume is
π/3 r^2h
= (π/3) (24*3)^2 (16*3)
= 82944π
V = 82944 cm^3
                    Answered by
            Roshan
            
    Steve's answer is incorrect.
In the final stage, he said (24*3)^2.
However, 24 is not the RADIUS of the cone's base. It is the DIAMETER.
Therefore, you must halve 24.
The final calculation should hence be:
V = (π/3) (12*3)^2 (16*3)
= 20736
    
In the final stage, he said (24*3)^2.
However, 24 is not the RADIUS of the cone's base. It is the DIAMETER.
Therefore, you must halve 24.
The final calculation should hence be:
V = (π/3) (12*3)^2 (16*3)
= 20736
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