Answer :
Final answer:
The area of the curved surface of the cone is 100.5 cm². The correct option is C)
Explanation:
To find the area of the curved surface of a cone, we need to know the slant height of the cone. Since the radius and height of the cone are in the ratio 4:3, let's assume that the radius is 4x and the height is 3x. We can use the Pythagorean theorem to find the slant height of the cone:
Slant height = sqrt((radius^2) + (height^2)) = sqrt(((4x)^2) + ((3x)^2)) = sqrt(16x^2 + 9x^2) = sqrt(25x^2) = 5x
The area of the curved surface of the cone can be found using the formula: Area = π * radius * slant height = π * (4x) * (5x) = 20πx^2
Given that the area of the base is 154 cm², we can find the value of x:
Area of the base = π * (radius^2) = π * (4x)^2 = 16πx^2 = 154 cm²
Solving for x: 16πx^2 = 154 cm². Divide both sides by 16π: x^2 = 9.625/π. Taking the square root of both sides, x ≈ 1.25
Now, we can substitute the value of x back into the formula for the area of the curved surface:
Area = 20πx^2 ≈ 20π(1.25)^2 ≈ 31.25π ≈ 98.07 cm²
Therefore, the area of the curved surface of the cone is approximately 98.07 cm².
The area of the base of the cone is given as 154 cm2, and the formula for the area of a circle is A = πr2, where A is the area and r is the radius. From the given area, we can find the radius of the base of the cone using the formula r = √(A/π). With the radius, we can use the given ratio of 4:3 between radius and height to find the height of the cone. To find the curved surface area of the cone, we will use the formula for the lateral surface area, A = πrl, where l is the slant height. We can find the slant height using the Pythagorean theorem applied to a right triangle with the radius and height as the perpendicular sides, which is, l = √(r2 + h2). Using these formulas and calculations, we can calculate the curved surface area of the cone.
