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.
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
To find the value of V, we can use the formulas for the curved surface area and volume of a cone:
The formula for the curved surface area of a cone is:
CSA = πrℓ,
where CSA is the curved surface area, r is the radius of the base, and ℓ is the slant height.
The formula for the volume of a cone is:
V = (1/3)πr^2h,
where V is the volume, r is the radius of the base, and h is the height.
Given that the diameter of the base is 24x cm, we can find the radius by dividing the diameter by 2:
radius (r) = diameter / 2 = 24x / 2 = 12x cm.
Given that the height of the cone is 16x cm, we can substitute the values of the radius (r) and height (h) into the formula for volume:
V = (1/3)π(12x)^2 * 16x = (1/3)π * 144x^2 * 16x = (1/3) * 2304πx^2.
Therefore, the value of V is 2304/3πx^2 cm^3.
To find the value of V, we need to calculate the volume of the cone and express it in the form Vπ.
The formula for the volume of a cone is given by:
Volume = (1/3) * base area * height
To begin, we need to find the base radius of the cone. Since the diameter is given as 24x cm, we can divide it by 2 to obtain the radius.
Radius = Diameter / 2 = 24x / 2 = 12x cm
Next, we can find the base area of the cone using the formula for the area of a circle.
Base Area = π * radius^2 = π * (12x)^2 = π * 144x^2
Now, we can substitute the given values into the formula for the volume:
Volume = (1/3) * Base Area * Height = (1/3) * (π * 144x^2) * (16x)
= (1/3) * 2304πx^3
Therefore, the value of V is 2304/3, which simplifies to 768.
So, V = 768.
The answer is in cm^3, not cm^2, as volume is a three-dimensional measure.
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