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