Calculate the curved surface area of a solid cone of base radius 14cm and vertical height 6cm
To calculate the curved surface area of a solid cone, we need to find the slant height first.
The slant height can be calculated using the Pythagorean theorem:
Slant height (l) = √(base radius^2 + height^2)
l = √(14^2 + 6^2)
l = √(196 + 36)
l = √232
l ≈ 15.26 cm
Now, we can calculate the curved surface area (CSA) using the formula:
CSA = π * base radius * slant height
CSA = π * 14 * 15.26
CSA ≈ 677.97 cm²
Therefore, the curved surface area of the solid cone is approximately 677.97 cm².
To calculate the curved surface area of a solid cone, we need to know the slant height of the cone. The slant height can be found using the Pythagorean theorem.
The Pythagorean theorem for a right triangle is given by:
c^2 = a^2 + b^2
In this case, the slant height (c) is the hypotenuse, the base radius (a) is one of the legs, and the vertical height (b) is the other leg.
Given:
Base radius (a) = 14 cm
Vertical height (b) = 6 cm
Let's find the slant height (c):
c^2 = a^2 + b^2
c^2 = (14 cm)^2 + (6 cm)^2
c^2 = 196 cm^2 + 36 cm^2
c^2 = 232 cm^2
Taking the square root of both sides:
c ≈ 15.23 cm (rounded to two decimal places)
Now that we have the slant height, we can calculate the curved surface area (CSA) of the cone using the formula:
CSA = π × a × c
Where π is the mathematical constant pi (approximately 3.14159), a is the base radius, and c is the slant height.
Substituting the given values:
CSA = π × 14 cm × 15.23 cm
CSA ≈ 677.62 cm^2 (rounded to two decimal places)
Therefore, the curved surface area of the solid cone is approximately 677.62 cm^2.
To calculate the curved surface area of a solid cone, you can use the formula:
Curved Surface Area = π * r * l
where:
- π is a mathematical constant approximately equal to 3.14159.
- r is the radius of the base of the cone.
- l is the slant height of the cone.
To find the slant height (l) of the cone, you can use the Pythagorean theorem. Since we have the radius (r) and the vertical height (h) of the cone, we can find the slant height (l) as follows:
l = √(r^2 + h^2)
Now, let's substitute the given values into the formula and solve the problem step by step:
Given:
Base radius (r) = 14 cm
Vertical height (h) = 6 cm
1. Calculating the slant height (l):
l = √(14^2 + 6^2)
l = √(196 + 36)
l = √232
l ≈ 15.26 cm (rounded to two decimal places)
2. Calculating the curved surface area:
Curved Surface Area = π * r * l
Curved Surface Area = 3.14159 * 14 * 15.26
Curved Surface Area ≈ 679.65 cm² (rounded to two decimal places)
Therefore, the curved surface area of the solid cone is approximately 679.65 cm².