A cone of height 24cm has a curved surface area 550 cm2 . Find its volume.
To find the volume of a cone, we first need to find its radius.
The curved surface area of a cone can be calculated using the formula:
CSA = π * r * ℓ
Where:
CSA = Curved Surface Area of the cone
r = radius of the cone's base
ℓ = slant height of the cone
In this case, the curved surface area (CSA) is given as 550 cm², and the height of the cone is given as 24 cm.
Now, the slant height (ℓ) can be found using the Pythagorean theorem, which applies to the right triangle formed by the height, radius, and slant height of the cone:
ℓ² = r² + h²
where:
h = height of the cone (given as 24 cm)
ℓ = slant height of the cone
r = radius of the cone's base
Substituting the given values, we get:
ℓ² = r² + 24²
ℓ² = r² + 576
Now, we can substitute this value of slant height (ℓ) into the formula for the CSA of the cone:
550 = π * r * ℓ
550 = π * r * √(r² + 576)
To find the volume of the cone, we can use the formula:
Volume = (1/3) * π * r² * h
Substituting the given value of height (h = 24) and solving for the radius (r), we can then substitute the value of radius into the volume formula to find the volume of the cone.