Find the surface area of a cone that has a radius of 13 m and a slant height of 27 m. Write your answer to two decimal places.
Question
Find the surface area of a cone that has a radius of 13 m and a slant height of 27 m. Write your answer to two decimal places.
Solution
The formula for the surface area of a cone is given by:
A = πr(r + l)
where:
- r is the radius of the base of the cone
- l is the slant height of the cone
Given that the radius r = 13 m and the slant height l = 27 m, we can substitute these values into the formula:
A = π * 13 * (13 + 27)
Now, calculate the expression in the parentheses:
A = π * 13 * 40
Then, multiply the numbers:
A = 520π
To get the numerical value, multiply this by the value of π (approximately 3.14):
A = 520 * 3.14
A = 1632 m²
So, the surface area of the cone is approximately 1632 square meters.
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