What is the lateral area of the cone to the nearest whole number.
Height: 50 m.
Diameter: 240 m.
First, we need to find the radius of the cone. We know that the diameter is 240 meters, so the radius is half of that, or 120 meters.
Next, we need to find the slant height of the cone. This can be found using the Pythagorean theorem with the height and radius:
slant height = sqrt(50^2 + 120^2) = 130.4 meters
Finally, we can calculate the lateral area of the cone using the formula:
lateral area = π × radius × slant height = 3.14 × 120 × 130.4 = 49,438.08 square meters
Rounding to the nearest whole number, the lateral area of the cone is approximately 49,438 square meters.
The slant height is exactly 130, not 130.4
A human would have realized that 50, 120, 130 is a multiple of the
standard 5-12-13 right-angled triangle
lateral area = π (130)(120) = appr 49,008.85 m^2
(you had 3.14 × 120 × 130.4 = 49,438.08, which should have been
49,159.64, using your wrong 130.4
So you have 2 errors in your solution !!!!! )
Thank you for pointing out those errors. You are correct, the slant height is exactly 130 meters and using the 5-12-13 triangle is a useful shortcut.
Using the correct values, the lateral area is:
lateral area = π × radius × slant height = 3.14 × 120 × 130 = 49,008.85 square meters
Rounded to the nearest whole number, the lateral area of the cone is approximately 49,009 square meters.
btw, where would you possible find a cone with that size ??
You are correct that a cone with a height of 50 meters and a diameter of 240 meters is a very large cone and not likely to be found in real life. It may be a hypothetical scenario or a math exercise designed to test one's understanding of cone geometry and calculations.
To find the lateral area of a cone, you need to calculate the slant height of the cone first. The slant height can be found using the Pythagorean theorem.
Step 1: Find the radius of the cone.
The diameter is given as 240 m, so the radius (r) can be calculated by dividing the diameter by 2:
r = 240 m / 2 = 120 m.
Step 2: Calculate the slant height.
The slant height (l) can be found using the Pythagorean theorem, which states that the square of the hypotenuse (l^2) is equal to the sum of the squares of the other two sides. In this case, one side is the height (h) of the cone (50 m), and the other side is the radius (r) of the base of the cone:
l^2 = r^2 + h^2
l^2 = 120^2 + 50^2
l^2 = 14400 + 2500
l^2 = 16900
l ≈ √16900
l ≈ 130 m (rounded to the nearest whole number).
Step 3: Calculate the lateral area of the cone.
The lateral area (A) of a cone can be found using the formula:
A = πrl,
where r is the radius of the base of the cone and l is the slant height.
A = π × 120 m × 130 m
A ≈ 50265.48 m^2 (rounded to two decimal places).
Therefore, the lateral area of the cone, to the nearest whole number, is 50,265 m^2.
To find the lateral area of a cone, you need to know the slant height or the slant angle. Unfortunately, you have not provided either of these measurements.
If you know the slant height (l), you can use the formula: Lateral Area = π * (radius) * (slant height).
If you know the slant angle (θ) in degrees, you can use the formula: Lateral Area = π * (radius) * (slant height) = π * (radius) * (2 * sin(θ/2)), where slant height = 2 * radius * sin(θ/2).
Since you haven't provided the slant height or angle, it's not possible to calculate the exact lateral area. Please provide the missing information, so I can help you find the answer.