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What is the lateral area of the cone to the nearest whole number? The figure is not drawn to

scale.

15,080 m2
25,133 m2
45,239 m2
50,265 m2

What is the lateral area of the cone to the nearest whole number? The figure is not-example-1
User Huski
by
4.2k points

2 Answers

4 votes

The lateral area of the cone to the nearest whole number is 25,133 m².

To find the lateral area of the cone, we need to use the formula:

Lateral Area = π * r * s

where:

π is pi (approximately 3.14)

r is the radius of the cone's base (half the width)

s is the slant height of the cone

Step 1: Calculate the radius

The radius is half the width of the cone's base, which is:

Radius = Width / 2

Radius = 160 m / 2

Radius = 80 m

Step 2: Calculate the slant height

We can use the Pythagorean theorem to find it. We know the height of the cone (60 m) and the radius (80 m). Slant height forms the hypotenuse of a right triangle with these two sides as legs. Therefore:

Slant height² = Height² + Radius²

Slant height² = 60² m² + 80² m²

Slant height² = 3600 m² + 6400 m²

Slant height² = 10000 m²

Slant height = √10000 m (taking the square root of both sides)

Slant height ≈ 100 m (rounded to the nearest whole number)

Step 3: Calculate the lateral area

Now that we have both the radius and the slant height, we can plug them into the formula:

Lateral Area = π * r * s

Lateral Area ≈ 3.14 * 80 m * 100 m

Lateral Area ≈ 25,133 m² (rounded to the nearest whole number)

Therefore, the lateral area of the cone to the nearest whole number is 25,133 m².

User Keith Miller
by
5.3k points
4 votes

Answer:

The lateral surface area of the cone is
25120\ m^2.

Explanation:

We have.

Height of a cone is 60 m

Diameter of a cone is 10 m

Radius, r = 80 m

The lateral surface area of a cone is given by :


A=\pi rl

l is slant height of the cone,


l=√(60^2+80^2) =100\ m

Plugging all values in above formula,


A=3.14* 80* 100\\\\A=25120\ m^2

So, the lateral surface area of the cone is
25120\ m^2.

User Noman Akhtar
by
4.2k points