Calculate the volume and curved surface area of a cone 14cm in base diameter and 24cm high
radius of base = 7 cm,
let the slant height be s
s^2 = 24^2 + 7^2
s = 25
V=(1/3)πr^2h = (1/3π)(49)(24) = 392π cm^3
SA = πrs = π(7)(24) = 392π cm^2
You didn't say if you want the circular base included, if so, add 49π cm^2
Vol=1/3 pie r^2h
=1/3x22/7x7^2x24
=1232cm^3
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To calculate the volume and curved surface area of a cone, you need to know the base diameter and the height of the cone.
Let's start with the volume of the cone. The formula for the volume of a cone is given as:
V = (1/3) * π * r^2 * h
Where V is the volume, π is a mathematical constant approximately equal to 3.14159, r is the radius of the base (half of the diameter), and h is the height of the cone.
Given the base diameter as 14cm, we find the radius by dividing it by 2:
r = 14cm / 2 = 7cm
Now, substitute the values into the formula:
V = (1/3) * π * (7cm)^2 * 24cm
V = (1/3) * 3.14159 * 49cm^2 * 24cm
Calculate the volume:
V ≈ 12336.2 cm³
So, the volume of the cone is approximately 12336.2 cm³.
Now let's move on to the curved surface area of the cone. The formula for the curved surface area is:
A = π * r * l
Where A is the curved surface area, π is the mathematical constant approximately equal to 3.14159, r is the radius of the base, and l is the slant height of the cone.
To find the slant height, we can use the Pythagorean theorem. The height of the cone and the radius form a right-angled triangle, where the slant height is the hypotenuse. So:
l = √(r^2 + h^2)
Given the radius as 7cm and the height as 24cm, substitute the values into the formula:
l = √(7cm^2 + 24cm^2)
Calculate the slant height:
l ≈ √(49cm^2 + 576cm^2)
l ≈ √625cm^2
l ≈ 25cm
Now, substitute the slant height and the radius into the formula for the curved surface area:
A = π * 7cm * 25cm
Calculate the curved surface area:
A ≈ 3.14159 * 7cm * 25cm
A ≈ 549.78 cm²
So, the curved surface area of the cone is approximately 549.78 cm².