Calculate the volume and surface area of a cone 14 cm in base diameter and 24 cm height
recall that v = 1/3 πr^2 h
or, since r = d/2, v = 1/12 πd^2 h
Now just plug in your numbers.
a = πr(r+s) = πr(r + √(r^2+h^2) )
To calculate the volume and surface area of a cone, we can use the following formulas:
1. Volume of a Cone:
The formula to calculate the volume of a cone is V = (1/3) * π * r² * h,
where V is the volume, π is a mathematical constant approximately equal to 3.14159, r is the radius of the base, and h is the height of the cone.
2. Surface Area of a Cone:
The formula to calculate the surface area of a cone is A = π * r * (r + l),
where A is the surface area, π is the mathematical constant, r is the radius of the base, and l is the slant height of the cone.
Now, let's calculate the volume and surface area using the given measurements:
Given:
Base Diameter = 14 cm
Height = 24 cm
First, we need to find the radius of the cone's base. Since the base diameter is given, we can divide it by 2 to get the radius.
Radius = Base Diameter / 2 = 14 cm / 2 = 7 cm
1. Volume of the Cone:
Using the formula V = (1/3) * π * r² * h, we substitute the values:
V = (1/3) * 3.14159 * 7² * 24
V = (1/3) * 3.14159 * 49 * 24
V = 3.14159 * 49 * 8
V ≈ 1,226.24 cm³
Therefore, the volume of the cone is approximately 1,226.24 cm³.
2. Surface Area of the Cone:
To calculate the surface area, we need to find the slant height (l) of the cone. We can use the Pythagorean theorem:
l = √(r² + h²)
l = √(7² + 24²)
l = √(49 + 576)
l = √625
l = 25 cm
Using the formula A = π * r * (r + l), we substitute the values:
A = 3.14159 * 7 * (7 + 25)
A = 3.14159 * 7 * 32
A ≈ 703.71642 cm²
Therefore, the surface area of the cone is approximately 703.71642 cm².