Find the lateral area of cone with a radius of 7ft and a slant height of 13 ft use 3.14 for round to the nearest tenth
1. 439.6 ft 2
2.324.5 ft 2
3. 571.5 ft 2
4.285.7 ft 2
explain why bot
h answer 1 and answer 3 are plausible:
To find the lateral area of a cone, we need to calculate the area of the curved surface. This can be done by multiplying the slant height by the circumference of the base:
Lateral Area = slant height x circumference of base
Circumference of base = 2 x pi x radius
Therefore, Lateral Area = slant height x 2 x pi x radius
Substituting the given values, we get:
Lateral Area = 13 x 2 x 3.14 x 7
Lateral Area = 571.5 ft^2 (rounded to the nearest tenth)
Answer 3 is correct, but Answer 1 is also plausible because it is close to the correct answer. However, Answer 1 may have been obtained by rounding off some intermediate calculations and hence may not be as accurate as Answer 3.
To find the lateral area of a cone, we need to use the formula:
Lateral Area = π * r * l
Where:
- π is a mathematical constant approximately equal to 3.14.
- r is the radius of the cone.
- l is the slant height of the cone.
In this case, the radius (r) is given as 7ft and the slant height (l) is given as 13ft.
So, substituting the given values into the formula, we have:
Lateral Area = 3.14 * 7ft * 13ft
Calculating this, we get:
Lateral Area = 285.7ft2
Therefore, the correct answer would be 4. 285.7ft2.