To find the surface area of the cone, we need to find the slant height first. The slant height can be found using the Pythagorean theorem:
(base)^2 + (height)^2 = (slant height)^2
In this case, the radius is given as 5 (which is the base) and the hypotenuse or side is given as 9 (which is the slant height). Let's plug these values into the equation:
(5)^2 + (height)^2 = (9)^2
25 + (height)^2 = 81
(height)^2 = 81 - 25
(height)^2 = 56
To find the height, we take the square root of both sides:
height = √(56)
height ≈ 7.5
Now that we know the height, we can calculate the surface area of the cone. The formula for the surface area of a cone is:
Surface Area = (pi) * (radius^2) + (pi) * (radius) * (slant height)
Surface Area = (3.14) * (5^2) + (3.14) * (5) * (9)
Surface Area = (3.14) * 25 + (3.14) * 5 * 9
Surface Area = 78.5 + 141.3
Surface Area ≈ 219.8
Therefore, the surface area of the cone is approximately 219.8 units squared.
Use the image to answer the question.
A cone shows a radius of 5 and hypotenuse or side as 9
What is the surface area of the cone? Use 3.14 for pi and round to the nearest tenth, if necessary.
1 answer