What is the surface area of the cone below figures are not drawn to scale round your answer to the nearest whole number
14 in radius
17 in
A. 628in 2
B. 578in 2
C.528 in2
D.1005 in2
The formula for the surface area of a cone is:
SA = πr² + πrs
where r is the radius of the base and s is the slant height of the cone. To find s, we can use the Pythagorean theorem:
s² = r² + h²
where h is the height of the cone. We're not given the height of the cone, but we can use the radius and the given slant height of 17 inches to find it:
h² = s² - r²
h² = 17² - 14²
h² = 225
h = 15
Now we can plug in the values we have into the formula for SA:
SA = π(14)² + π(14)(17)
SA = π(196) + π(238)
SA = 194.89 + 747.7
SA = 942.59
Rounding to the nearest whole number, the surface area of the cone is 943 square inches, which is closest to answer choice D.
Therefore, the correct answer is D. 1005 in2.
To calculate the surface area of a cone, you need to use the formula:
Surface Area = π * r * (r + l)
Where:
π is a constant approximately equal to 3.14159
r is the radius of the base of the cone
l is the slant height of the cone
In this case:
Radius (r) = 14 in
Slant height (l) = 17 in
Substituting these values into the formula, we get:
Surface Area = 3.14159 * 14 * (14 + 17)
Surface Area ≈ 3.14159 * 14 * 31
Surface Area ≈ 1371.72 in²
Since we need to round to the nearest whole number, the surface area is approximately 1372 in².
Therefore, the correct answer, when rounded to the nearest whole number, is option D. 1005 in².